Explanation
The WORKDAY function calculates dates in the future or past that are (by definition) "workdays". In other words, WORKDAY automatically excludes weekends and (optionally) holidays. WORKDAY accepts 3 arguments: start_date, days, and an (optionally) holidays.
Since we want to check a single date and get a TRUE or FALSE result, we would ideally use WORKDAY with the simple formula below:
=WORKDAY(date,0)
However, this doesn't work, since WORKDAY does not seem to evaluate a date when no offset is present.
The solution is supply (date-1) for start_date, 1 for days, and the named range "holidays" (E5:E6) for holidays.
This causes WORKDAY to step back one day, then add 1 day to the result, taking into account weekends and holidays. Effectively, we are "tricking" WORKDAY into evaluating the start_date.
When the date falls on a weekend or holiday, WEEKDAY will automatically adjust the date forward to the next working day.
Finally, we compare the original start_date to the the result of the WORKDAY function. If the dates are the same (i.e. the result of WORKDAY equals the start_date, the formula returns TRUE. If not, the formula returns FALSE.
Ensure a calculated date falls on a workday
To make sure any calculated date lands on a business day, you can use the following formula:
=WORKDAY(calc_date-1,1,holidays)
Note - if you need custom weekends, use the WORKDAY.INTL function.