Can my Sprint iPhone 5 be flashed to Metro PCS?

I recently got a iPhone 5 and I want it to be used with Metro, is it possible?

Perhaps.

T-Mobile bought Metro so they will soon be a GSM provider.

A flashed phone will work on their CDMA network but once T-Mobile shuts it down in 2015 a flashed phone will no longer work on GSM networks.

Since the iPhone 5 is an international device, it can (illegally) be unlocked to work on GSM networks but I'm not sure that a flashed CDMA device can be unlocked.

Your best bet is to stay with Sprint.