I guess because the Skillcd column is an integer the IN wasn't working but I switched it to this and it's working now.

Distinct(
    SortByColumns(
        Filter(
            'Personnel.PersonMasters',
            TermFlag = false &&
            (
                SkillCd = "0934" ||
                SkillCd = "0027" ||
                SkillCd = "0840" ||
                SkillCd = "0962" ||
                SkillCd = "0526"
            )
        ),
        "DisplayName",
        "Ascending"
    ),
    DisplayName
)