T4 contains deductions which you can make a claim on, plus it contains your cpp info (even if it's zero), ei info and
retirement contribution which is a vital part for rrsp purchasing...

and God forbid, should you need to apply for ei in the future, there is no record of employment if you use T5s,

I am gonna assume your employer had not deducted tax from your pay cheque, then tell him to give you neither documents, no records, no tax