iPhone Jail broken 5.1.1 can I upgrade to a jail broken 7.0 or above?

Nope.

You can upgrade to the latest Apple is signing. You'll lose your jailbreak. But anything other than the latest, no.

Alfiooo said:

Can you upgrade to 7.0 and above?

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I guess, the first question here should be....what iPhone do you have?

Alfiooo said:

Can you upgrade to 7.0 and above?

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iPhone 4, of course as 7.1.2 is the latest firmware offered.

Can the OP not simply just perform a restore via iTunes? It will remove the jailbreak however.

If he has an iPhone 4, he can save SHSH blobs, and make a custom IPSW

He never said what type of device he's using.
So all assumptions are pointless.

Alfiooo said:

Sorry I should of said it's a iPhone 4. So it can be done?

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Yes. Apple stopped upgrading the iPhone 4 at iOS 7.1.2. The only problem is the performance of the device will drop noticeably from 5.1.x to 7.1.2.

Worth upgrading to iOS 7 though seeing as most apps are iOS 7 now

Alfiooo said:

When you say it will drop noticibly? Is that mainly battery life?

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No.
Everything will feel slow or lag compared to ios 5 that you're on now.

Plug it to the latest itunes and hit restore.
Then restore your backup and sync your stuff back.
Then jb it.

I would really advise against iOS 7 on an iPhone 4, My friends who did it ended up getting new phones because it made the 4 agonizingly slow!