Unless I have missed something, there has not much said about expected shape(s) for 5NT and 6C. How many suits are suggested by these bids?
If 5NT suggests 3 suits, then you probably have a club void so maybe there is not much point in using 6C to show a club void that you could have shown with 5NT (unless maybe it is a "Serious 5NT" situation

- 6C is a grand slam try in spades with first round club control
- 5NT then 6S is a grand slam try in spades lacking first round club control
(There is more to making this playable than what is written above)
If 5NT could also suggest only two suits (presumably a montrous 6-4 hand that may or may not have a club void), you can't use 5NT then 6S as a grand slam try. In this case, if you think a grand slam try in spades is important to have, you still might want to consider using 6C for this purpose.
Yes I know it is obscure to think of catering to hands that are interested in 7S but it is also obscure to think of catering to monstrous 3-suited hands that are interested in 7whatever.
This is hard stuff that becomes much harder when you consider that everything is different if the opening bid was 1H or the overcall was 5D.
Fred Gitelman
Bridge Base Inc.
www.bridgebase.com