The quintile and biquintile aspects happen when the angle between two astral items is respectively 72° and 144°. Most astrologers interpret them the same way.
In a birth chart, it is about vocation and creativity. It's the energy that motivates explorers and missionaries. It can also point at a talent or a gift. It is the desire to construct, the vision of the entrepreneur, the achievements of genuises and innovators.
These aspects reveal personality traits. They are obvious for those surrounding the bearer. They are part of what makes you stand out in the crowd, unique. They are not defense mechanisms or any attempt to compensate for some real or perceived flaw. It is genuine energy.
Quintile and biquintiles are the energies of fascination for a field of study or an area of interest. It's about analyzing and decomposing patterns and structures, and then recomposing and reconnecting them in creative ways. When one does not make a career path from this interest, it is often conveyed into a hobby or a passion. There is an urge need to find a creative outlet.
In transits, they can initiate new paths, new approaches. Thinking out of the box for once. They can trigger the start of new projects or endeavors. They can signal a departure from tradition and conservative attitudes. During such transits, you could get to understand your role in life, your mission on this planet.
In synastry, when such aspects exist between partners, they contribute very positively to the chemistry. They are meant to work together on some creative projects or visions.
Other minor & rare aspects: grand-cross, grand trine, quincunx & inconjunct, semi-sextile, semi-square, sesquisquare, t-square and yod