Agree with Standard - CTOT is for the aircraft, -5/+10 is to give ATC some flexibility in how we sort them out (I've had 3 aircraft with the same CTOT before - it's down to me to decide in which order they go, not the pilots).
If it's patently obvious the aircraft won't make the tolerance then you have two options:
1) Aircraft has to file a DLA and then ATC / Handling send a ready to see if they can improve on any slot given.
2) ATC speak to the Flow man at the ATCC - sometimes you can get an extra 5 minutes on top (and sometimes you can't, in which case option (1) above applies)
(Top tip - DON'T file a DLA unless we ask you to - just in case we've got you that extra "5" on your previous plan & CTOT)
Don't forget - CTOT stands for Calculated Take Off Time - it's the airborne time that counts, not the time you push back from the gate. The Captain should have known this (it's hardly rocket science after all). I've had crews try the same thing with me, thinking they can push back, start, taxi and be airborne in 4 minutes (It takes about 8 where I work) and are obviously annoyed when they get told they won't with a grudging "I suppose you know better".
Them's the rules - learn them, abide by them.