Can you fully charge a super capacitor at a lower voltage (than its max rating)
@Curd is right. "fully charged" bears no meaning.

Often, it just means that the capacitor voltage reached (of came very close to) the supply voltage. So, in this case, yes, you can fully charge it, at whatever voltage you want.

Now, if you want it to mean "store as much energy as it possibly could without exploding", then, no, and you'd better not even attempt to fully charge it.

In fact, you'd better ensure there is a small margin between the supply voltage and the capacitor rating. Using 6V/5.5V rated capacitors with a 5V supply seems reasonable (unless the 5V supply has a 20% tolerance, in which case you should use even higher ratings).