Slope intercept form means that you have to solve for y.
Subtract 5x from both sides
5x - 6y - 5x = 22 - 5x
= -6y = 22 - 5x
Then divide by -6
-6y/-6 = 22/-6 - 5x/-6
= y = -22/6 + 5x/6
You can reduce the fraction -22/6 to -11/3
y = -11/3 + 5x/6
Then swap the order of your terms so it looks nicer and you don't have a negative in front
y = 5x/6 - 11/3