As mentioned by others, calendar and forum (seems to be most prominent on site) will have things to look into but overall at first glance not to difficult.
This is based on what i see, not what happens inside.
If wysiwig (tiny) was used when creating pages etc.. this could throw off the actual content settings.
Calendar less prominent it seems, so suppose you loose function on it? would that be ok?
Forum is present, so that is the one ( pages and members of course too ) are the ones to focus on.
Of course theme...is something different. There's a 3 column piece (colors of course and bg) RideBlue from
our Jimako that poses the overall appearance, else i would suggest plain bootstrap 3. (just some ideas).
Question becomes.. iff your not in a hurry i could look at it, and iff you want to do it yourself i can give pointers.
Personally (if i think a noticed correctly what happens on site), the best outcome would give a fresh install, and manually populate the tables out of the old ones..(carefully).
Depending of how the pages were created, it could mean a lot of work correcting placements of text and images..(helas iff so, but it is present). You always may contact me via PM (click user).
@Jimako : yes php 7 and onwards would be the case i guess, but once (think upgrade vs fresh) done on php 5.3 and than switch to 7 (maybe correct new issues iff happens) one is good to go from there up to php 8 etc.. (each php version in 7 has some quircks itself) as base is set ..