Nope - 7805 him give 5.0 volts (according to Fairchild's datasheet anyway).
7805 him give 5 volts only when him not knackered.
A working one should be fine. If the ground line gets disconnected, the thing has nothing to refer to, so the voltage can rise to the supply voltage. Now it gets technical - not all 7805s are identical between manufacturers or even batches. Some can turn into a disconnection (no volts out), others might well turn into a direct connection (full volts out). When working properly, they all behave like the data sheet says, under fault conditions, either inside the plastic or in the circuit around them, its toss a coin in the air time. Maybe best of three.
Digging the 7805 out will show whether the supply volts will stay where it belongs or whether there is another path giving the trouble.
The thing is though, even if it was bought on the strength of a vendors specification, without anything to actually identify it, it is a box of unknown capability, so a known replacement is the safest bet for a valuable model.