If two lines are perpendicular, their slopes are negative reciprocals of one another. Applying this here: If the new line is to be perpendicular to the one whose slope is -5, then the new line must have the slope +1/5 (the negative reciprocal of -5).
The new line passes through (3,2). Let's take all the info we have and solve for the y-intercept, b, of the new line:
general slope-intercept formula for a str. line is y=mx+b.
Here we have x=3 and y=2, as well as m=1/5.
Then 2 = (1/5)(3)+b
Clear out the fractions by multiplying all 3 terms by 5: 5(2) = 5(1/5)(3) + b.
Then 10 = 3 + b; b=7.
The equation of the new line is then y=(1/5)x+7.