A.A.
"He is tired at the end of a long week in school, but that's not an acceptable excuse."
I think it's understandable for him to act this way at the end of a long week. It's not a great excuse, but for a 5-year-old, it is a reasonable explanation. I would try to spend time suggesting his emotions like "It seems like you're tired (or mad, or frustrated). Maybe you'll feel better with " fill-in-the-blank... some rest, a good meal, some mom time, whatever. It's also really important IMHO to describe what made him mad, ask him if that's true from his perspective, try to mirror his feelings and show them to him.
It's okay to give some slack when he's crabby. I like people to give me some slack when I'm crabby too, and I'm a grown-up with much greater understanding than my 5-year-old. :)