This is a good place for an introduction to skill-level based pars. That 5 on hole 3 is for Green tees, which are appropriate for players rated 800 or lower – emphasis usually on lower. Hole 3 has an appropriate Blue (950-rated) par of 3.
Every hole can be assigned a par for every skill level, but usually only the par for the intended skill level is shown.
One of the problems with pars at tournaments is that the TD will just adopt the course par – which was probably set for Blue or White level players – and use it for Open players, which, I think, have earned the right to have the TD figure out and use Gold par.
The game could certainly function without par. It could also function without measuring the length of holes. But, the game is better with both being available and accurate.
Most people who dismiss par use an argument that is analogous to "Not all tee signs have accurate hole lengths, so hole length is irrelevant."
For an extremely easy-to-3-for-its length hole, a hole could be up to 1000 feet long and be par 3 for Gold, or 800 feet for Blue. Those are extreme examples, like down a ski hill or something. But, I've designed 500+ foot par 3s at the Blue and Gold level.
Dunderheads unite!