Question: when I hire an electrician to swap out the old fusebox with a
circuit breaker box, can I also have that socket five circuit split
into separate circuits?

Depends on how the wire runs to the rooms. If the split for them is at the
box, sure you can have it easily setup on it's own circuit. But if the
split is further along in the rooms then you'll have to run new wire. It's
likely at least a few runs will need new wire as designers of older homes
had quite different expectations about electrical use.