We've just gone over this thoroughly in the sim a few days ago with my company. We make the V1 call slightly before V1, because the decision to go/stop must be made by V1. If you get the call at V1, it's too late.
We did a limiting takeoff in the sim, where the engine failed about two seconds before V1 but kept going and the plane took off just fine.
Five seconds sounds excessive to me, but as long as it's before that's a good thing.