53 — pterygovaginal artery.  Master diagram and labels here

A very small artery in the upper nasopharynx.  The area is extensively supplied by various vessels, including the accessory meningeal (53a), superior division of the pharyngeal trunk of the ascending pharyngeal (51),  and vidian / mandibulovidian (52) arteries.  Remember balance — any one of these can be dominant, co-dominant, etc.

There are three small named arteries projecting posteriorly from the terminal IMAX: from superior to inferior they are artery of foramen rotundum, vidian artery, and pterygovaginal artery.  The latter two supply upper mesial nasopharynx around the eustacian tube.

Here is a prominent Pterygovaginal artery (53) on common carotid injection

DYNA CTs are very helpful here

One of typical vessels supplying JNAs — see full case here

Pterygovaginal is the main vessel projecting posteriorly from the terminal IMAX