Equidistant in this case means that the distance from (0, b) to (5, 5) is the same as the distance from (0, b) to (3, -2).
The distance from (0, b) to (5, 5) is
\(\sqrt{(0-5)^2+(b-5)^2} = \sqrt{25 + (b-5)^2}\).
The distance from (0, b) to (3, -2) is
\(\sqrt{(0-3)^2+(b+2)^2} = \sqrt{9 + (b+2)^2}\)
These two distances are equal to each other, so
\(\sqrt{25 + (b-5)^2} = \sqrt{9 + (b+2)^2} \\
25 + (b-5)^2 = 9 + (b+2)^2 \\
25 + b^2-10b+25 = 9 + b^2 + 4b + 4 \\
-14b = -37 \\
b = 37/14\)
