Reportedly see ex around Peruvian city peak (6)

I believe the answer is:

climax

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'peruvian city peak' is the definition.
'climax' can be an answer for 'peak' (I've seen this before). I'm unsure of the 'peruvian city' bit.

'reportedly see ex around' is the wordplay.
'reportedly' becomes 'lima' (I can't justify this - if you can you should believe this answer much more).
'see' becomes 'C' (the word for the letter, according to Chambers).
'ex' becomes 'x'.
'around' is an insertion indicator.
'c'+'x'='cx'
'lima' inserted into 'cx' is 'CLIMAX'.

Can you help me to learn more?

(Other definitions for climax that I've seen before include "Turning point or culmination" , "Exciting conclusion" , "Turning point, moment of greatest intensity" , "Peak of emotion" , "exciting finale" .)

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

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