Update my iPhone 5 jailbreak?

So, I have my iPhone 5 running on a jailbroken iOS 6.1 (I know, old school). I know there isn't a jailbreak for 7.1 out (and it seems like there won't be), but is there any way to update my iPhone to a more recent version that is able to be jailbroken (like iOS 7.0.6)?

Added (1). P.S: I did try googling this first, but I didn't come up with many results (but I'm also not sure how to properly word my google search haha)

I'm not sure if you can, because Apple wouldn't sign your iOS version and so it wouldn't install it. Of there's any way, you'd have to download the iOS.ipsw of the version you want and select to update from that file. But like I said, because Apple stopped signing those versions, it might refuse to update.

I think your better off installing iOS 7 themes and stuff like that.