Use the point slope formula...
The slope is 4.
Indeed, the veracity/validity/whatever of the point slope formula should not be called into question at this juncture. So we're left with the task of finding a point and a slope, in order to determine the desired line.
Welp, g(5)=-3 means that (5, -3) is the point.
And you really DO need to know that the slope of the tangent is given by the derivative.