let

d = the age of Derrick

b = the age of Brandon

Derrick is 5 less than twice as old as Brandon:

d = 2b - 5

The sum of there ages is 31:

d + b = 31

by solving the system of equations:

d = 2b - 5

d + b = 31

we find:

d = 19 years

b = 12 years

click here to see the step by step solution of the system of equations:

Derrick is 19 years old and Brandon is 12 years old.