Is your 3V input 3VP-P, 3VP or 3Vrms?
If it is 3VP-P, then it should be just fine as Nigel said. If it is 3VP, you will have to either go to a rail-rail op amp as #12 said, but raise the supply rails by a few hundred mV to avoid all clipping of the signal OR raise the supply rails to overcome the limitations of your existing op amp. If it is 3Vrms, then your looking at an input of nearly 8.5VP-P so a gain of 5 would yield a potential of ~42.2VP-P, which puts the effective value (rms) of the output right at the rail.