The WORKDAY formula is fully automatic. Given a date and days, it will add days to the date, taking into account weekends and, optionally, holidays.
In this case, holidays are supplied as the named range holidays (E4:E8), so holidays are taken into account as well. Notice that Excel only cares about holiday dates, not holiday names.
WORKDAY defines a weekend as Saturday and Sunday. If you need more flexibility, use the WORKDAY.INTL function instead.