The styles of a great many poems (5)
I believe the answer is:
modes
'the styles' is the definition.
('mode' can be a synonym of 'style')
'many poems' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'poems' becomes 'odes' (ode is a kind of poem).
'm'+'odes'='MODES'
'of a great' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for modes that I've seen before include "Ways - manners" , "Fashions" , "Styles of domes" , "Styles (in clothes, etc)" .)