Game birds seen after the fifth of October (5)
I believe the answer is:
bowls
'game' is the definition.
(I know that bowls is a type of bowling)
'birds seen after the fifth of october' is the wordplay.
'birds' becomes 'owls' (owl is a kind of bird).
'seen after' means one lot of letters go next to another.
'the fifth of october' becomes 'b' (5th letter of 'october').
'owls' put after 'b' is 'BOWLS'.
(Other definitions for bowls that I've seen before include "Containers for fruit" , "They're rolled towards jack" , "Throws or rolls a ball" , "woods" , "Rolls smoothly along the ground" .)