I’ve noticed that some Ashkenazi communities (including those following minhag lita and minhag polin) will sometimes swap the order of which days of selichot are said during the Aseret Yemei Teshuvah.
In a year when Yom Kippur falls on a Monday or a Thursday, they will recite the selichot printed for the ‘fifth day’ of the Aseret Yemei Teshuvah the day before those printed for the ‘fourth day’ of the Aseret Yemei Teshuvah.
What is the reason for this custom?
With full thanks and acknowledgement to @JoelK, it writes in Nitei Gavriel here the following:
כשחל יוה"כ ביום ב' או ביום ה' יש מקדימים לומר סליחות של י"ג מדות ביום ב' או ביום ה' שלפניו, כדי שיאמרו הסליחות של י"ג מדות ביום שיש בו קרה"ת ויש מקומות שנוהגים אשר רק אם חל בשבת מקדימים ליום ה', אבל כשחל ביום אחר א"צ לשנות, ויש מקומות שאין משנים בשום ענין וכל מקום נוהג כמנהגו
When Yom Kippur falls on a Monday or a Thursday, some bring forward the selichos that we say of the 13 middos on the Monday or Thursday before, in order that these selichos of the 13 middos are said on a day in which there is Torah reading. And there are some places that are accustomed to do so only if [the day before Erev Yom Kippur] falls on shabbos then they bring these selichos forward to Thursday, but when it falls on another day, one does not need to change. And there are some places that don't change at all. In all instances, every place should do like their custom.
