Time expression: "Quarter of"

[rowrrbazzle]

The OED on “of” (excerpt).

The primary sense was ‘away’, ‘away from’, a sense now obsolete, except in so far as it is retained under the spelling off (see OFF adv., prep., n.1, and adj.). All the existing uses of of are derivative; many so remote as to retain no trace of the original sense, and so weakened as to be in themselves the expression of relatively indefinable syntactic relationships.

The OED says “off” is derived from “of” (excerpt).

< OF prep. (see etymological note s.v.).

Developed from the strong form of OF prep., the word regularly has final /f/. Both weak and strong forms are used for OF prep. until the 17th cent., at which time the two words become fully differentiated. Off is uncommon in Old English, and is used with greater frequency only after c1400.

This is consistent with something I read once, that “of” was originally pronounced just like “off”, unlike our pronouncing it as “uv”.

So as already stated, “quarter of 5” is an archaic usage that means one quarter of an hour away from 5.