Need to update Word Press but don’t want to mess anything up

Hi,

This site I’ve just been give the reigns of has an ancient version of Word Press. They severly stated they didn’t want any thing to happen to any of the content. I’ve backed up the HTML folder.

Is this okay to up date now? How do I update? It’s so old that there’s no easy way to do it. Do I have to delete the files?

Thanks,

Richard