5-12-13 and square!

Geometry Level 2

$$ABCD$$ is a square with $$AB=13$$. Points $$E$$ and $$F$$ are exterior to $$ABCD$$ such that $$BE=DF=5$$ and $$AE=CF=12$$.

If the length of $$EF$$ can be represented as $$a\sqrt b,$$ where $$a$$ and $$b$$ are positive integers and $$b$$ is not divisible by the square of any prime, then find $$ab$$.

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