Is this normal?

I'm new to Civ 5 (avid Civ 4 player). Playing vanilla.

I've just come out the other end of a war against 6 civs, 5 of which D.O.W. me in the same turn, and managed to sue for peace with most of them after a good 40 or 50 turns.

The thing that was unusual was the peace settlements I managed to get.

Russia's was understandable as I took four of there cities, but the 3 other peace treaties I negotiated were with Civ's I never physically fought with as they were a huge distance away, but they were all willing to offer me 3 or 4 of there cities, all there gold, gold per turn, any available luxury and strategic resources + open borders.

Obviously I didn't take the offer of their cities but everything else, just seems way too much. The game has gone from me thinking things were over to thinking I've found an exploit by accident.

Is it normal?

Yeah, AI is stupid. This happens sometimes.

Oh well, I guess I'll just go with it and look at using a mod once I've got a bit more experience with vanilla.

Cheers for the reply.

Relative army strengths and empire sizes are taken into account and are weighted higher than and who fares better in the fighting. I'm guessing you're first in most of the demographics.