Your husband sounds stressed. Just because something is normal at any given age doesn't mean it can't be annoying or shouldn't be corrected.
You could have told your son to 'please use a whisper voice while we are waking up'. If my son was yelling while I was asleep, I'd be pissed off too. We have taught our son that you don't get to wake up sleeping people unless there is an emergency, you are hurt, bleeding, throwing up, etc. It's rude and inconsiderate and your husband had every right to be annoyed. It's a natural consequence if you think about it. He's not two, he's not three-- he's old enough to come in quietly to check in with you.
Maybe you both have different expectations of your son? I would have told my son to use a whisper voice and taken him out if *I* didn't have the expectation that a five year old is capable of being quiet enough, not expected the sleeping person to just be cool with being wakened. Being abrupt or angry is a pretty natural response. I hate being wakened 'just because'.
You say your husband is busting his hump to get his work done, and he sounds stressed out. I don't think you need to walk on eggshells, but I do think your son needs some boundaries. Maybe your husband can set up an 'office' in a quiet part of the house so they don't disrupt each other.
Also, maybe it's time to talk to a counselor. Sometimes, people are stressed and need better coping mechanisms. Does he feel that you have his back when it comes to discipline? It can be hard when one parent feels like they are addressing unwelcome behaviors when the other parent seems to be ignoring it or letting it go. So, when you can get a date or find some child-free, stress-free time, try to problem-solve with your guy. What is the thing he's finding most annoying-- and tell him you will help in addressing that. Even if it isn't your hill to die on, back him up because it might be worth it in the long run.
I'll also say this: five is time for kindergarten. It's time to have some age-appropriate, reasonable expectations. Kindergarten teachers, too, may focus on behaviors you feel are 'fine', and they will also need your back. This is a part of kids growing up-- it's not all about them.