Which major key corresponds to 5 flats or 7 sharps?

The major key that corresponds to 5 flats or 7 sharps is D flat Major. This key signature is derived from the Circle of Fifths, which is a fundamental concept in music theory. Each key signature can be represented in two different ways, depending on whether you count flats or sharps.

For D flat Major, the key signature includes the notes D flat, E flat, F, G flat, A flat, which adds up to 5 flats. Alternatively, if one were to move to the enharmonic equivalent of D flat Major, which is C sharp Major, it consists of 7 sharps: C sharp, D sharp, E sharp (which is F), F sharp, G sharp, A sharp, and B sharp (which is C). Therefore, both key signatures represent the same sound but in different tonal contexts, confirming that D flat Major is indeed the correct answer for the question regarding 5 flats.

In this instance, while C sharp Major has 7 sharps, it doesn't apply when specifically looking for the key with 5 flats, which further supports why D flat Major is the appropriate choice here.