Nope. The supply voltage is the limit. There's no way the opamp can create a higher voltage than its supply. You mention rail-to-rail, by which you mean the difference between positive and negative supply. But rail-to-rail in opamps also has a different meaning. A rail-to-rail output opamp will have its maximum output close to the positive power supply (minus a few tens of mV) and the minimum output close to \$V_-\$. If you have a regular opamp the maximum output will be 1.5V to 2V less than \$V_+\$, so in your case +3V to +3.5V. That's for 1V in. Look up output voltage swing in the datasheet. Note that for a +5V single supply the output range will be limited to something like 2V to 3V, which may be of little use. For such low supply voltages in general a rail-to-rail opamp is used.
RRIO is an often used abbreviation which means rail-to-rail I/O. Means that also the input voltage can go close to the rails and still will be properly processed. Non-RRIO opamps will allow these voltages, but won't amplify them properly.
Don't apply 10V in, and certainly not 100V in. Most opamp will break if your inputs are beyond the rails (outside of 0V..5V in your case).