I have three 15-amp breakers, twelve 20-amp breakers, two 30-amp breakers, and two 40-amp breakers in my main panel with a 200-amp main breaker.

Can I upgrade the two 40-amp circuits to 50-amp without overloading the panel?

I need to know the answer before I buy the larger capacity cable and breakers for those two circuits.

The number on the breaker is meaningless. It's the actual load you have to worry about.
From the look of it though you'll have no issues doing what you want. Why are you replacing these circuits with larger?