Precalculus, Chapter 6, 6.3, Section 6.3, Problem 42

Hence, you need to find the unit vector having the same direction as the vector v = <5,-12> , hence, you need to use the formula, such that:
u = v/|v|
You need to evaluate the magnitude |v|, such that:
|v| = sqrt(a^2+b^2)
|v| = sqrt(5^2 + (-12)^2) => |v| = sqrt(25+144) => |v| = sqrt 169 => |v| = 13
u = (<5,-12>)/13 => u = <5/13, -12/13>
You need to check that the magnitude of the unit vector is 1, such that:
|u| = sqrt((5/13)^2 + (-12/13)^2)
|u| = sqrt(25/169 + 144/169)
|u| = sqrt ((25+144)/169)
|u| = sqrt (169/169)
|u| = sqrt 1
|u| = 1
Hence, evaluated the unit vector yields u = <5/13, -12/13>.