Club is in district of Washington and capital of Ohio (5)
I believe the answer is:
disco
'club' is the definition.
(I know that club can be written as disco)
'district of washington and capital of ohio' is the wordplay.
'district of washington' becomes 'disc' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'and' says to put letters next to each other.
'capital of' suggests taking the first letters.
The initial letter of 'ohio' is 'o'.
'disc'+'o'='DISCO'
'is in' is the link.
Can you help me to learn more?
(Other definitions for disco that I've seen before include "Musical party" , "Modern dance hall or event, in brief" , "Music genre - dance venue" , "Club or party with dancing" , "1970s' musical genre" .)