SELECT DATE_ADD(`date_field`, INTERVAL 5 DAY) As FinalDate
FROM `table_name`;

SELECT DATE_ADD(
    date_field,
    INTERVAL 5 +
    IF(
        (WEEK(date_field) <> WEEK(DATE_ADD(date_field, INTERVAL 5 DAY)))
        OR (WEEKDAY(DATE_ADD(date_field, INTERVAL 5 DAY)) IN (5, 6)),
        2,
        0)
    DAY
    ) AS FinalDate
FROM `table_name`;

SELECT
@ID:='2017-10-04' as initial_date, -- the initial date in the right format to manipulate (add x day)
@DTA:=20 as days_to_add, -- number of days to add
@DA:= DATE_ADD(@ID, INTERVAL @DTA DAY) as date_add,
@LASTDAY := WEEKDAY(@DA) as last_day, -- the day (Monday, Tuesday...) corresponding to the initial date + number of days to add
@WEEK1 := DATE_FORMAT(@ID, '%v') as initial_date_week, -- format the initial date to match week mode 3 (Monday 1-53)
@WEEK2 := DATE_FORMAT(@DA, '%v') as added_date_week_nbr, -- the week # of the initial_date + number of days to add
@WEEKDIFF := @WEEK2 - @WEEK1 as week_difference, -- the difference between week 2 and week 1
DATE_ADD(@ID,
        INTERVAL @DTA +
            if ( @WEEKDIFF > 0 or @LASTDAY in (5,6),
              2,
              0
              ) +
             if (@WEEKDIFF > 1,
             @WEEKDIFF*2,
             0
             ) DAY
    ) AS FinalDate