I have recently set 5 minutes in a 500,000sq ft warehouse for wardens to verify a pre alarm before it escalates to evacuation. Breaking an MCP goes to immediate evacuation. I think in this case I have been conservative- sprinklers and HSSD throughout, and a calculated ASET( without sprinklers) of 16 minutes. So my 5 minutes came from 5 minutes to verify, 3 minutes to respond and evacuate ( fire wardens to gee people up) plus 100% safety margin= 16 minutes. In this case the detection and sprinklers were a bonus- in a building this large it would possibly take at least 5 minutes for a fire to be detected by the occupiers anyway.
I think that for a conventional building designed around the ADB/ 5588 template, 7 minutes would usually be too long. But if you have calculated an ASET then I cant see any problem in working within the time available, povided there is some safety margin, which needs to take both the management procedures and sods law into acount.