It's always better to replace components before they fail, and five years isn't bad going for a battery. If you have the funds, then why not?
On the other hand, if it's working well then it would probably happily go on for another couple of years.
But now that you've thought of it, wouldn't it be a complete PITA if you didn't replace it and it let you down?
If it were me I'd stick a new one in and keep the old one as a spare for the electric fence on the chicken run.
