You can still Rex in Civ 5, how much depends on difficulty, how fast depends on your civ and how large in the end depends on the map (and size).
The trick is to micro manage your cities and workers, never puppet a conquered city and don't rely on city state bonuses for anything more than a boost. Personally, I skip maritime city states entirely and focus instead on cultural (for obvious reasons) and militaristic for a steady supply of units to gift to city states. The most important bonus from city states is their resources, so ally with those that have luxury resources you don't have and strategic resourced you need for your military. Ignore the rest until/unless you are going for a diplo victory. Once you have some experience you can mess with maritime states as a way to boost specialist counts or burust pop growth when you get a bunch of surplus hapiness.
Social policies depend on what you plan on doing with your large empire. Although Piety looks like a no-brainer at first glance it's not as good for large empires as you may think, you'll rarely have surplus happiness in any significant quantity and while two free policies is nice the cost to get their isn't always worth it. The bonus to population hapiness in non-conquered cities is great... unless half your empire is conquered cities. The military caste policy in the honor branch is handy when you have your steamroller running, garrison units in newely conquered cities to keep you above the -10 threshold, pull them out and conquer more cities when it's safe to do so. Honor, Commerce, Order and Autocracy are my favorites for large empires, the 33% reduction in unit maintenance can be a massive boost to your income and double stretegic resource quantity including oil and aluminum? Sign me up
Keep in mind that I spend most of my game at war, it's difficult to grow beyond a handfull of cities without conquest so anything that makes war and production more efficient is worth more in the long run.
Certain civs are definately superior choices for large empires. The obvious ones being China, Russia and Songhai for their UB bonuses or Arabia, America, India, Iroquois and Persia for their special abilities (yes, India). It will work with any civ though, just don't expect that same degree of success when playing as the Aztec
Population control is essential. In epic speed games on large maps my general rule from the start is that no city grows larger than then number of high value tiles around it. This means I can thrive with cities spaced 2-3 tiles apart and pull in immense profits from the trade routes while also hitting the point where the majority of my individual cities generate more happiness than they use. There will be exceptions, such as a city alongside a winding river throguh hills with some food resources as that will be a production monster with a hydro plant, railroad connection and factory. You will do better to avoid the giant 'gold' city surrounded by trading posts as the cost in happiness won't be worth it compared to the same revenue form spreading the population out amongst 4-5 cities each with their own trade route, happiness buildings and culture buildings.
So the general strategy is to grow your capital until it can work all of the best tiles around it and then start pumping out settlers until you have 5-6 cities (or however many you can support without going below -10 happiness). Each city should be building/purchasing the basic buildings and units you'll need to continue expanding. Do not get caught in the trap where you focus too much on buildings and stop building up your military. Gold buildings (market, bank, etc) are almost always worth building as are happiness buildings. There is no pre-set build order, you need to be flexible and adjust as the situation demands, perhaps happiness is more critical than culture so you can put off buying or building that monument for a while.
Eventually, every city will be able to work a minimum of 7 tiles (city center +6 surrounding) so your goal is to get every city up to that size or as large as needed to work all of the prime tiles around them. Size 6 is a good minimum as that will give you very good trade route income and your science output will be substantial with a large empire of 6 pop cities. Planned economy will take care of the unhapiness of the number of cities so be ready for a growth spurt in the industrial age.
With this number of cities China's paper maker will dwarf the +1 g per trade route that arabia receives. Consider my last game as China on a large map (small continents) where I had 62 cities, all of them with a paper maker in them. Likewise the culture output from Songhai with their maintenance free mosque is impressive with a similar empire.
Production can be very good too, even in the small cities. With +3 per coastal city and +5 per city even a single tile island city with four fish/pearls/whales will have a base production of 18 hammers (with a seaport), base income of 18 gold and enough food to support 7 pop (so 4 tile workers and 3 specialists) or 9 if you build a lighthouse, 11 with a granary.
The final large empire trick is golden ages. You should be working a massive number of tiles compared to a small empire, the sudden boost of gold and production can be insane. Unfortunately it's very hard to grow large and maintain surplus happiness so you end up relying on great people and the Taj Mahal but in comparison the net gain from each golden age will be so much that it should easily overcome the ability of smaller empires to hit more frequent golden ages due to excess happiness.
The trick is to micro manage your cities and workers, never puppet a conquered city and don't rely on city state bonuses for anything more than a boost. Personally, I skip maritime city states entirely and focus instead on cultural (for obvious reasons) and militaristic for a steady supply of units to gift to city states. The most important bonus from city states is their resources, so ally with those that have luxury resources you don't have and strategic resourced you need for your military. Ignore the rest until/unless you are going for a diplo victory. Once you have some experience you can mess with maritime states as a way to boost specialist counts or burust pop growth when you get a bunch of surplus hapiness.
Social policies depend on what you plan on doing with your large empire. Although Piety looks like a no-brainer at first glance it's not as good for large empires as you may think, you'll rarely have surplus happiness in any significant quantity and while two free policies is nice the cost to get their isn't always worth it. The bonus to population hapiness in non-conquered cities is great... unless half your empire is conquered cities. The military caste policy in the honor branch is handy when you have your steamroller running, garrison units in newely conquered cities to keep you above the -10 threshold, pull them out and conquer more cities when it's safe to do so. Honor, Commerce, Order and Autocracy are my favorites for large empires, the 33% reduction in unit maintenance can be a massive boost to your income and double stretegic resource quantity including oil and aluminum? Sign me up
Keep in mind that I spend most of my game at war, it's difficult to grow beyond a handfull of cities without conquest so anything that makes war and production more efficient is worth more in the long run.Certain civs are definately superior choices for large empires. The obvious ones being China, Russia and Songhai for their UB bonuses or Arabia, America, India, Iroquois and Persia for their special abilities (yes, India). It will work with any civ though, just don't expect that same degree of success when playing as the Aztec
Population control is essential. In epic speed games on large maps my general rule from the start is that no city grows larger than then number of high value tiles around it. This means I can thrive with cities spaced 2-3 tiles apart and pull in immense profits from the trade routes while also hitting the point where the majority of my individual cities generate more happiness than they use. There will be exceptions, such as a city alongside a winding river throguh hills with some food resources as that will be a production monster with a hydro plant, railroad connection and factory. You will do better to avoid the giant 'gold' city surrounded by trading posts as the cost in happiness won't be worth it compared to the same revenue form spreading the population out amongst 4-5 cities each with their own trade route, happiness buildings and culture buildings.
So the general strategy is to grow your capital until it can work all of the best tiles around it and then start pumping out settlers until you have 5-6 cities (or however many you can support without going below -10 happiness). Each city should be building/purchasing the basic buildings and units you'll need to continue expanding. Do not get caught in the trap where you focus too much on buildings and stop building up your military. Gold buildings (market, bank, etc) are almost always worth building as are happiness buildings. There is no pre-set build order, you need to be flexible and adjust as the situation demands, perhaps happiness is more critical than culture so you can put off buying or building that monument for a while.
Eventually, every city will be able to work a minimum of 7 tiles (city center +6 surrounding) so your goal is to get every city up to that size or as large as needed to work all of the prime tiles around them. Size 6 is a good minimum as that will give you very good trade route income and your science output will be substantial with a large empire of 6 pop cities. Planned economy will take care of the unhapiness of the number of cities so be ready for a growth spurt in the industrial age.
With this number of cities China's paper maker will dwarf the +1 g per trade route that arabia receives. Consider my last game as China on a large map (small continents) where I had 62 cities, all of them with a paper maker in them. Likewise the culture output from Songhai with their maintenance free mosque is impressive with a similar empire.
Production can be very good too, even in the small cities. With +3 per coastal city and +5 per city even a single tile island city with four fish/pearls/whales will have a base production of 18 hammers (with a seaport), base income of 18 gold and enough food to support 7 pop (so 4 tile workers and 3 specialists) or 9 if you build a lighthouse, 11 with a granary.
The final large empire trick is golden ages. You should be working a massive number of tiles compared to a small empire, the sudden boost of gold and production can be insane. Unfortunately it's very hard to grow large and maintain surplus happiness so you end up relying on great people and the Taj Mahal but in comparison the net gain from each golden age will be so much that it should easily overcome the ability of smaller empires to hit more frequent golden ages due to excess happiness.
