Civ4 used a % chance system, so a tank had a 99.9% chance of beating a spear, so it wasn't likely a spear could win, but its possible. Also a large number of spears could plough into the tank damaging it each time and eventually get a good % chance to kill it.
In civ5, we can't be sure how the combat results are determined, it may still use some kind of "chance" factor, but then again it might not, it certainly doesn't show it. I think civ5 may very well deal in certainties as can be shown below.
The end result is shown before the combat, the battle result is determined, the health loss is calculated, and its all shown, so one can summarise the random % chance of loss is gone, which In my opinion is a good thing, it only ever frustrated me.
But what is clear is that units that lose still deal out damage according to thier strength figure, so while the "1 in 1000 spearmen's victory" is gone, the other issue from civ4 was that a spearman could greatly injure the tank even though it couldnt really win. Now instead of this being a random chance too and the amount of damage random as it appeared to be in civ4, it is actually calculated and shown, and is relative to strength. So depending on the strength of a spearman will depend how many would need to be sacraficed in bringing the tanks health down. While we don't have the strength of a spearman, it should be about half that of the pikeman, and we know its strength.
So as we can clearly see (assuming a spear is half the strength of the pike, it could be a little higher like 1.5 time's less) then the tank will be 9-12 ish times stronger in strength, which means technically if a tank does nothing, doesnt heal, doesnt run off, doesnt upgrade with all the kills 10-15 spears could kill the tank. But in civ5 that would be a sizeable army of spears
If a tank was all alone in the middle of your terriotry you could surround it with 18 spears, (2 hex wide circle) and attack the next turn but generally the tank will be in a line with other units and then depending if its on a poking out hex or poking in hex or a striaght hex, it can only be attacked by 4 units in the safer "in position", 7 spears able to attack in the straight position and still only 11 spears in the "out" position. (Which may not be enough to kill it) So technically, unless your an idiot, you probably wont ever have spears killing tanks without other units helping out.
What I meant by "in" or "out" or "straight" is simple, a line in a hex grid can either be vertical, (which has in and out points), "sort of diagonal" which is a striaght line, or horizontal, which is a straight line, see
Click