5d and 6d SCFTs Have No Weak Coupling Limit

We prove that there does not exist any weak coupling limit in the space of superconformal field theories in five and six dimensions, based on an analysis of the representation theory of the corresponding superconformal algebras. Holographically, this implies that superstring theories on AdS${}_6$ and AdS${}_7$ do not admit tensionless limits. Finally, we discuss the implications of our result on the existence of an action for coincident M5-branes.