2a + 3b = 5
b = a - 5
what is a and b?

Since you have your b term, you can start off by plugging it in where b is in the first equation.
2a +3(a-5) = 5

Distribute the 3 to the "a" and -5.
2a + 3a - 15 = 5

Now you can combine your "a" terms
5a - 15 = 5
 
Next you want to get the "a" term alone so you can add 15 to both sides.
5a - 15+15 = 5+15
5a = 20

Now divide both sides by 5 to get your "a" value.
5a = 20
/5
a = 4

Now that you have your "a" value, all you have to do is plug your "a" value into either equation. I personally would choose the second equation since it's easier.

b= 4-5
b= -1

You can go back and check by plugging your answers back into the first equation as well!
2(4) + 3(-1) = 5
8 -3 = 5
5 = 5

a = 4 and b = -1