Explanation
Working from the inside out, the YEAR, MONTH, and DAY functions extract those respective date components:
=YEAR(B5) // 1960
=MONTH(B5) // 3
=DAY(B5) // 8
At the outer level, the DATE function simply reassembles the component values back into a valid Excel date. To add years to the date, we just need to add the value in C5 to the year component prior to reassembly:
=DATE(YEAR(B5)+C5,MONTH(B5),DAY(B5))
The formula is then solved like this:
=DATE(1960+10,3,8)
=DATE(1970,3,8)
=8-Mar-1970
Note: if you need to add an "even" multiple of 12 months to a date (i.e. 12, 24, 36, 48, etc) you can use a much simpler formula based on the EDATE function. See: add months to a date.