Seventy two degrees is a fifth of the circle, and the quintile is the aspect that fifth produces. It has no place in Hellenistic or medieval doctrine, which recognised only the divisions by one, two, three, four and six. It was proposed by Johannes Kepler, who was looking for aspects on the basis of the regular polygons that can be inscribed in a circle and the musical ratios those divisions correspond to, and who added the quintile, the biquintile and several others on that reasoning.
The justification matters because it is a different kind of justification. The classical aspects were defended by their relation to the signs: a trine joins signs of one element, a square joins signs of one mode. The quintile joins nothing in particular, because five does not divide twelve. Two planets seventy two degrees apart may stand in signs that are in aversion to one another, so a quintile can exist between planets that traditional doctrine says cannot see each other at all. Kepler was not troubled by this, having already set aside the sign-based account.
Modern usage keeps the quintile on a narrow orb, typically one to two degrees, and associates it with craft, style and a facility that is developed rather than given. That association is a twentieth century accretion, not something Kepler stated, and it circulates chiefly through the harmonic school. The honest summary is that the quintile is a real division of the circle with a short and traceable history, and that most of the meaning attached to it is younger than the aspect itself.