May sway ... (5)
I believe the answer is:
might
This clue is a double definition.
'may' is the first definition.
('may' and 'might' are similar in meaning)
'sway' is the second definition.
(thesaurus)
(Other definitions for might that I've seen before include "- - and main" , "Force; could" , "Strength - could possibly" , "is not unlikely to" , "Clout" .)