label your unknown numbers
I'm calling them x and y
x+y=21
5x+2y=66
find a relation of x and y
y=21-x
substitute this into your second equation
5x+2 (21-x)=66
simplify to find x
5x+42-2x=66
3x+42=66
3x=24
x=24/3=8
apply your findings to find the second number
8+y=21
y=13
check your answer
5 (8)+2 (13)=66
40+26=66
we now know that the first number x is 8
and the second number y is 13