To get the Slope-Intercept form of a line, you first need to put it into Point-Slope form, which is

where

and

are the given coordinates and m is the given slope. So, plug your given information into the equation.
y + 3 = 5 (x + 2) Use the Distributive Property
y + 3 = 5x + 10 Subtract 3 from both sides
y = 5x + 7