That's not correct. The terms 2a and 3b are not like terms, so we cannot combine them to get 5ab. We simply leave it as 2a+3b.
If you had 2a+3a, then it would simplify to 5a
Similarly, 2b+3b = 5b
Or you could have 2ab+3ab = 5ab
The key is that the variable portions must match up to be able to add them.