Quite a lot of the music I like seems to be on 5 string basses, so I'd like to play 5 string eventually.
Jump right in! I Squier Affinity Jazz V will set you back about $180, and it is a decent instrument. By the time you get around having enough for an upgrade you will be well ahead of the curve. If you don't care for it you won't have the urge to scratch that (5 string) itch anymore.
I started on a 4 string. Bought a 5ver because I wanted to move to 5 strings "eventually", and it quickly became my main player.