The larger of two numbers is 10 less than five times the smaller number. the sum of the two numbers is 86. find the two numbers.

Consider a number 10 larger than the larger of the two numbers. It will be 5 times the smaller, and its sum with the smaller will be 96 (that is, 10 more than 86). Then the smaller number is 1/(1+5)×96 = 16. The larger number is 86-16 = 70

smaller number: 16
larger number: 70

_____
You can write equations
  y = 5x - 10
  y + x = 86
Substitute the first equation into the second:
  5x - 10 + x = 86
  6x = 96
  x = 16 . . . . as above