Problem with a century plant (5)
I believe the answer is:
sumac
'plant' is the definition.
The answer is an example.
'problem with a century' is the wordplay.
'problem' becomes 'sum' (arithmetic problem).
'with' is a charade indicator (letters next to each other).
'century' becomes 'C' (common abbreviation).
'sum'+'a'+'c'='SUMAC'
(Other definitions for sumac that I've seen before include "Shrub or small tree - Camus (anag)" , "Tree or shrub; reverse of French writer" , "Novelist" , "Garden shrub" , "Rhus tree" .)