For part a, we need to get the equation to be y=mx+b, so we do the following:
5x-3y=15
5x-3ycolor(red)(+3y)=15color(red)(+3y)
5xcolor(red)(-15)=15+3ycolor(red)(-15)
(5x-15)/color(red)(3)=(3y)/color(red)(3)
5/3x-5=y
For part b, we know that in the equation y=mx+b m is the slope, so from our equation in a we know that 5/3 is the slope.
For part c, we know that in the equation y=mx+b the y-intercept is at (0,b), so our point is at (0,-5)
For part d, we combine parts c and b to know that we start at (0,-5) and go up 5 and across 3 (slope of 5/3). Another way to graph it is by taking the equation we were given and setting x=0 and finding y and then setting y=0 and finding x, those are your intercepts and can be graphed to create a line equal to the one you want.
Hope this helped!