I think the Computed Column Specification does not allow aggregation (Min, Max,...). You can try something like below. If 12/31/2099 > that the date dateadd([year],[col5],[col6]) then we can assume that the later is a min date, else the former is the min date
DECLARE @DateCom TABLE(
[Year] [int] NULL,
[Col5] [int] NULL,
[Col6] [date] NULL,
[Col7] AS (case when dateadd(year,[col5],[col6])<'12/31/2099' then dateadd(year,[col5],[col6]) else '12/31/2099' end)
)
INSERT INTO @DateCom
SELECT 2018, 2, '2018-01-01' UNION
SELECT 2018, 3, '2011-01-01' UNION
SELECT 2014, 10, '2017-08-25' UNION
SELECT 2017, 1, '2017-08-25' UNION
SELECT 2020, 100, '2020-01-01'
SELECT * FROM @DateCom
OUTPUT:
Year Col5 Col6 Col7
2014 10 2017-08-25 2027-08-25
2017 1 2017-08-25 2018-08-25
2018 2 2018-01-01 2020-01-01
2018 3 2011-01-01 2014-01-01
2020 100 2020-01-01 2099-12-31