Can anyone tell me why this IF formula isn't working?

=IF(D5<E5<F5,"A",IF(D5E5F5,"B",
IF(D5<E5F5,"C",IF(D5E5<F5,"D","F"))))

It's returning "B" every time. D5, E5, and F5 are all derived from
formulas. Is that the problem? I appreciate any help!