Moves slowly to provide sides with slight advantages (5)
I believe the answer is:
edges
I believe this is a triple definition!
'moves slowly' is the first definition.
(I've seen this in another clue)
'to provide' is a link.
'sides' is the second definition.
(edge is a kind of side)
'with' is a link.
'slight advantages' is the third definition.
(I've seen this in another clue)
(Other definitions for edges that I've seen before include "They're used for cutting" , "Slowly moves" , "Inches" , "Outside limits" , "Boundaries of a surface" .)