jmc

The diagonals of a rhombus divide the rhombus into four congruent right triangles, the legs of which are half-diagonals of the rhombus. Let $a$ and $b$ be the half-diagonal lengths of the rhombus. The area of the rhombus is 4 times the area of one of the right triangles, in other words $4\times \frac{1}{2}ab=2ab$. Since $a=5$ units and the area of the rhombus is $120$ square units, we find $b=120/(2\cdot 5)=12$ units. The perimeter is 4 times the hypotenuse of one of the right triangles: $$\text{Perimeter}=4\sqrt{a^2+b^2}=4\sqrt{5^2+12^2}=4\cdot 13=\boxed{52}\text{ units}.$$