Because the angles at both sides of the x are the same, to find the angle you need to make the equations into:
4x+7=5(x-4)
To solve this, first you need to use the distributive property.
4x+7=5x-20
Then you combine like terms. Since they're on different sides of the equal sign you subtract the smallest term from the biggest term.
7=x-20
Then you do inverse operations and add 20 to both sides.
27=x
Therefore, the value of x is 27.