One’s being very slow to accumulate (5)
I believe the answer is:
amass
'to accumulate' is the definition.
('amass' can be a synonym of 'accumulate')
'one's being very slow' is the wordplay.
'one's' becomes 'am' ('one is' can humorously mean 'I am').
'being very slow' becomes 'ass' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'am'+'ass'='AMASS'
Can you help me to learn more?
(Other definitions for amass that I've seen before include "Build up" , "Gather together, pile up" , "store" , "run up?" , "Get together" .)