The first thing is that a 7805 is not an adjustable voltage regulator, and even if it was, that circuit is not the way to do it.
Get a 7812, or something like an LM317 with the correct circuit.
The other possible issue is that transformer cannot supply sufficient current. You need to tell us the current (or VA) rating of the transformer. In your case a 1A or about 15VA would be the minimum I'd be happy with.
I'd also recommend a higher current bridge because the peak currents you'll be drawing each half cycle will probably be in excess of 1A.