Parallel lines refers to a pair of straight lines that never intercept or touch each other. The slopes of this lines is the same one.
On this exercise is given the equation of a line, and is asked to find the slope of a line that is parallel to the given one.
5x-3y=1 Subtract 5x in both sides
-3y=-5x+1 Divide by -3 in both sides to isolate y
y=5/3x-1/3
The slope of the given line, 5x-3y=1, is 5/3, which means that the slope of a line parallel to this one, would be 5/3.