There are several customs that relate to Yahrtzeit, such as lighting a candle, saying Keil Malei Rachamim, etc. These typically are done on the Yahrtzeit, though some do it on the preceding Shabbos.
Which day is counted for a person who died Bein HaShemashos? Do we go after the preceding day, or the following day? That is, if they died during the Bein HaShemashos between the fifth and the sixth, is the Yahrtzeit observed on the fifth or the sixth?
Even for customs not observed on the Yahrtzeit itself, there are practical applications. If the fifth is a Wednesday and the sixth is a Thursday, is Keil Malei Rachamim said on Monday or Thursday leining? If the fifth is a Friday and the sixth is a Shabbos, for those who light on the previous Erev Shabbos, in which week is it lit?