How to unlock my jailbroken iPhone 5 so that I can use any sim card?

Carrier I was with does not do that

Have you tried any one of the online unlocking service?
It's one of the alternative idea when you carrier doesn't provide unlocking service. For cheapest unlocking visit http://www.mobile-unlocker.com/apple-iphone-5/rs5wp9/ They will provide an unlocking service for particular locked carriers only.