Slots
If you have been issued with a CTOT (restricted slot) then you have a -5/+10 minutes window. You also have to take into consideration the taxi allocation.
For example if you have been issued with a 12:10Z CTOT and at an airport with a 15 minute taxi time allocation, your window to request engine start is between 11:50Z & 12:05Z.
With an ETOT (unrestricted slot) I believe its technically -15/+15 minutes, however I beleive at several locations they go on -30/+30 minutes.
Cheers,
Buzzz