How to jailbreak already jailbroken ios 6.1 iPhone 5?

My iPhone 5 is already running 6.1 ios jailbroken. I do not have iTunes installed and wish to avoid doing so if possible, as it causes performance issues for my PC.

Obviously I'd prefer to keep existing data on my phone if that's possible.

Added (1). It's ios7 (jailbrokenb) I wish to upgrade to

Why would you need to jailbreak an already jailbroken device?

iTunes isn't involved in the jailbreaking process anyhow, but of course should be installed to help manage the device better.