Game half century by a German (5)
I believe the answer is:
lotto
'game' is the definition.
(the UK National Lottery)
'half century by a german' is the wordplay.
'half century' becomes 'L' (Roman numeral for 50).
'by' says to put letters next to each other.
'a german' becomes 'otto' (common German name).
'l'+'otto'='LOTTO'
(Other definitions for lotto that I've seen before include "Housey-housey, bingo" , "gamble" , "Game in which numbers are drawn" , "Children's game; lottery" , "form of gambling" .)