change battery exactly on the fifth year?

[zzyzzx]

Do batteries need to be replaced the fifth year exactly on the date of installation?

NO!

can they last longer?

YES!

If you lived someplace that's really hot like South Texas / South Florida / Arizona, etc. my answers might be different.

 

[PandaBear]

Depends. My Prius' battery is 10 years now and still work well (not for starter duty obviously). My other cars' battery last between 6-9 years OEM Panasonic from Japan to about 2 years from the cheapest Walmart 1 year warranty ones.