He finally won tears from acts of self-aggrandizement (3-5)

I believe the answer is:

ego-trips

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

'acts of self-aggrandizement' is the definition.
'ego trips' can be an answer for 'acts' (ego trip is a kind of act). I'm not certain of the 'of self-aggrandizement' bit.

'he finally won tears' is the wordplay.
'finally' says to take the final letters.
'won' becomes 'got' (I've seen this in another clue).
'tears' becomes 'rips' (rip is a kind of tear).
The last letter of 'he' is 'e'.
'e'+'got'+'rips'='EGO-TRIPS'

'from' is the link.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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