Angry newborn?

All babies cry in different ways but sometimes my baby cries and seems angry. Is that normal? For example, sometimes he has a hard time latching on and when that happens he gets frustrated after 5 minutes and starts crying in an angry way and waving his little hands around and sometimes he would grab my arm and squeeze it and it feels like he's pinching me. He's 5 weeks old. I just wanted to see if other babies do that too?