One of the worst aspects of Civ5 is that you cannot randomly declare war on other civs, you're bound by the game mechanics, so if you're negotiated peace for X many turns through peace treaties then you cannot do any actions which initiate war, that includes moving inside their territory (unless you have an open bordered agreement) or attacking their units.
Remember that peace treaties can be negotiated between you and other civs through the trading menu, so they might offer up peace treaty as part of some larger deal that involves trading money and other goods.
Are peace treaties inherented from civs working together? I'm not sure...it's plausible that if you're at peace with someone you might inherent their peace treaties, a more advanced civ player can probably confirm that I'm never sure because I always ignore diplomacy and just stop other civs
Ehh, not sure how accurate some of that is. It's been a while since I fired up Civ5, but I played a decent amount of it. To my recollection, any time you make peace with a civ there is a mandatory 10 turn non-aggression agreement (and it's always 10 turns, non-negotiable, iirc), meaning neither civ can declare war on the other or engage in actions that would normally result in a declaration of war (like entering their borders without an open borders agreement, or attacking their units/cities).
I am fairly sure that you can not enter into any such pact in any other way, there are no treaties or agreements that prevent you from declaring war on any civ at any time other than the mandatory one that comes at the end of a war. I can't be 100% certain of this, but I'm pretty close to it.
The only time I can think of where you might unwittingly enter into such a treaty I suppose would be if you had been dragged into a multi-nation conflict by an ally. Often times once the main instigators of the war make peace (usually two AI civs), everyone who got dragged into the war makes peace with everyone else very soon after, and if you weren't a very active participant in the war you probably just agreed to their terms without even thinking about it, since it was probably just a straight up 'agree to end the war' deal with no concessions from either side.