let 'x' and 'y' be the numbers

one number is 5 more than 3 times another

x = 5 + 3y

the sum of the numbers is 13

x + y = 13

by solving the system of equations

x = 5 + 3y

x + y = 13

we find

x = 11

y = 2

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

the two numbers are 11 and 2.