It's going to be tricky, as you can't directly use GROUP BY in an UPDATE statement (UPDATE doesn't allow aggregate functions.
But... you could use A JOIN to a SELECT...GROUP BY but even then, it's going to be complicated, because you need the SELECT to return the row ID values together with a number you can use in the ADDDAYS function to generate the date code.
The last bit is relatively easy:
ROW_NUMBER (Transact-SQL) | Microsoft Docs[
^] will give you that if you use modulus 5 with it.
But it's going to be complicated to work out, and complicated to maintain and modify.
I'd be tempted to say this should be done in presentation software, rather than in SQL purely so it's easier to read!