The emitter is always going to be a few hundred milli volts behind the base voltage (in this type of configuration) and as the base voltage is 5V, depending on how much current is taken by the "switched" circuit" on the emitter, it is more likely to be 4.5V despite the collector being at 5V.
However, if you used a PNP transistor with the emitter being fed by the 5V there is a fairly good chance that you can attain 5V (less maybe 10 or 20 millivolts) on the collector (load side) without much hassle.
Better still use a P channel FET because this will do a slightly better job (maybe only a couple of millivolts "lost") and it can be fed directly from a 5V logic supply to its gate. Source will connect to incoming 5V and output will be on drain.