In Just Intonation, 5/4 is the frequency ratio between the 5th and 4th harmonics. Measuring about 386.3¢, it is about 13.7¢ away from 12edo's major third of 400¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for 5-limit harmony. It is distinguished from the Pythagorean major third of 81/64 by the syntonic comma of 81/80, which measures about 21.5¢. 81/64 and 5/4 are both just intonation "major thirds," 81/64 having a more active and discordant quality, 5/4 sounding more "restful".
In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated here melodically in singing into a resonant udderbot (from the fundamental up to 5 and then noodling between 5 and 4).
5/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314...
5/4 the interval, like all intervals, refers to a relation between two pitches. It has been called the just major third to distinguish it from the other intervals in that neighborhood.