Audacity of the courts installing Democrat in district (4,2,3,5)
I believe the answer is:
neck of the woods
'district' is the definition.
(someone's neck of the woods is their neighbourhood)
'audacity of the courts installing democrat' is the wordplay.
'audacity' becomes 'neck' (I've seen this before).
'courts' becomes 'woos' (woo can mean to court romantically).
'installing' indicates putting letters inside (I've seen this in other clues).
'democrat' becomes 'd'.
'woos' going around 'd' is 'woods'.
'neck'+'of'+'the'+'woods'='NECK OF THE WOODS'
'in' acts as a link.
(Another definition for neck of the woods that I've seen is " perhaps in a particular area".)