G'day,
I'll make an assumption that you're flying a 172, Warrior or similar. I'll put in a disclaimer that it's been many years since I've flown a single engine aircraft.
I can understand that while you're training, things like run-ups take a bit longer than once you're more experienced, but 5-7 minutes seems excessive. Run-ups are normally only required on the first flight of the day, NOT prior to every take-off, despite what some flying schools say.
I can't think of any valid reasons to do run-ups while on the threshold of a runway. Whoever gave you that opinion is wrong, IMHO!
In your other scenario, perhaps you've got a point, but any aircraft taxiing up behind you (presumably you've made some kind of broadcast that you're stopping on the taxiway to do run-ups) shouldn't come so close as to be affected by your prop-wash.
My Opinion:
Find somewhere on the apron that is appropriate and out of the way. That is, somewhere your prop-wash isn't going into a hangar, passenger movement area, parked aircraft, etc. Taxi there. Use your Situational awareness (e.g. looking over your shoulder) to check no-one's come up behind you, and do your run-ups.
Another opinion (once you're more experienced) do your run-ups while taxiing. Not an issue in a 172, Warrior or similar.
DIVOSH!