Let us assume the larger number be x and the smaller number be y

According to the question, we have:

x + y = 80 …(i)

x = 4y + 5

x – 4y = 5 …(ii)

Now, by subtracting (ii) form (i) we get

5y = 75

y = 15

Putting the value of y in (i), we get

x + 15 = 80

x = 80 – 15

x = 65

Hence, the two numbers be 65 and 15