Jockey reported winning, bagging Cheltenham's first trophy (5,3)

I believe the answer is:

ryder cup

I'm a little stuck... Click here to teach me more about this clue!

'trophy' is the definition.
(I've seen this before)

'jockey reported winning bagging cheltenham's' is the wordplay.
'jockey' becomes 'rider' (horse rider).
'reported' shows a homophone (sound like).
'winning bagging cheltenham' becomes 'cup' (I can't justify this - if you can you should believe this answer much more).
'rider' sounds like 'ryder'.
'ryder'+'cup'='RYDER CUP'

'first' acts as a link.

Can you help me to learn more?

(Other definitions for ryder cup that I've seen before include "US-Europe golf event" , "Golfing contest" , "Prize for golfers" , "trophy" , "Sporting event" .)

I've seen this clue in The Times.

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