let

x = the first number

y = the second number

one number is one more than a second number:

x = 1 + y

five times the first is 8 les than 4 times the second:

5x = 4y - 8

by solving the system of equations

x = 1 + y

5x = 4y - 8

we find

x = -12

y = -13

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