Can i jailbreak my iphone 5 running ios7 and its unlocked using rsim?

Can i jailbreak my iphone 5 running ios7 and its unlocked using rsim?

Yes this is the best jailbreak for iso7 and totally free
http://evasi0n.com/

Yes, the RSim unlock should work, depending on the version. You should better get your phone factory unlocked though as you can then update firmware as you wish.