I agree, using the first shot as an aiming point means that it's not actually a 5 shot group. EDIT: And good point, like you say it can't even be counted as a four shot group, because you don't know which shot was the aiming point.
Each shot is intended to hit a target (or a point offset from the target by using scope adjustment, if one wants to keep the aiming point clean). Each shot will land some distance away from the target, with that distance representing some combination of mechanical accuracy limitations, shooter skill, and wind. A five shot group is the sum of errors from five shots.
If you just randomly shoot a shot at paper and then use the hole as an aiming point, then that first shot by definition is the target, and thus doesn't contribute to the sum of errors in a group. Arguing that it does is circular reasoning (begging the question). I like using blue sharpie to make little dots as aiming points. If I were to draw a 0.22" circle in blue sharpie on paper and use it as the aiming point for 4 shots, can I call it a 5 shot group?
However, in general (but not in this challenge) you can use a bullet hole as an aiming point. If I were to do that I'd shoot a shot, adjust my scope to +5 MOA elevation, and then shoot 5 shots while aiming at that first bullet hole. That would give me a 5-shot group located 2.5" above my aiming shot (assuming this is 50 yds).