Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers ?

Let's denote the two numbers as x and y.

According to the problem, we have two equations:

1. The difference between two numbers is 5, which can be written as: x - y = 5

2. Six times of the smaller lacks by 6 from the four times of the greater. This can be written as: 6y = 4x - 6

Now, we can solve these two equations to find the values of x and y.

First, let's isolate x in the first equation: x = y + 5

Then, substitute x in the second equation: 6y = 4(y + 5) - 6 6y = 4y + 20 - 6 6y = 4y + 14 2y = 14 y = 7

Substitute y = 7 in the first equation: x = 7 + 5 x = 12

So, the two numbers are 12 and 7.