First understand that being five is hard, it is the cusp of being a big kid and not being a toddler. Kids pick up on things from parents, he will mimic what he sees, if you are compulsive about germs he will be too. I am a former big time germaphobe, I had to stop being so freaked out as I saw my kids washing their hands so much it caused rashes. I just had to explain them when it is important to wash, step out of my box and comfort zone and be calmer about the germ factor. Germs can be good to a degree, builds healthy immune system and you cannot prevent germs. Degerming too much can backfire too. It is very normal at this age though to pick up a "habit" and have it be hard. It doesn't always mean OCD though. My daughter went through it too. They teach about germs in school, then they hear it at home and kind of go overboard. For my daughter she got past this stage. It is very normal.
My four year old washes his hands a lot, too much and we had to reel him back in. He was not rinsing well and got a very sore red rash from too much soap, that is when I realized I needed to change my behavior. I blame myself due to me watching other kids too I can kind of get military on them about washing after the bathroom, before meals, when coming inside from school or playing outside. I just explain when it is important and over doing it too much leads to problems, stripping protective skin, causing infection if you wash too much.
Five year olds are tough too in the sense they want control and structure, it is normal it really is. His fits need to have consequences that matter, to help him learn self control. I have a seven year old I am still working on that with. It doesn't necessarily mean OCD.
You can have him evaluated, but just realize too it is very normal for a five year old to want what they want when they want it!!!! The best thing you can do to help him, is teaching him calming techniques, when he is feeling angry, validate his anger but also tell him he cannot act out and help him calm down. When he pitches a fit, have a consequence. The best gift you can give him now is hold him accountable for is actions, do not cater to him, do not ever cave when he pitches a fit, but give him consequences for bad behavior. Reward the positive behavior.
If you are diagnosed with OCD, then you need to talk to your Dr about medications to help control it, if you just think you are then maybe both of you should get evaluated as there are ways to help both of you. Just remember he can just be picking up on your cues of germs. It is hard, I was never one to worry much until I had kids, then it is a different ballgame. I really went overboard, lysolling shoes, keeping shoes off the carpet, washing constantly, being ultra paranoid.
Now I just try to worry about what I can control and keep things in check, I know they will get sick, they will get germs no matter how careful I am and it isn't a bad thing all the time.