So
Qwark28 mind explaining how you approach the DS matchup , it's interesting you think it's 5-5 , personally i think it's 6-4 ( slightly advantage , if i wanted to be more "precise" i'd put it 5.5-4.5 but let's scratch that ) , the projectile game is in DS favour , LGS goes under Jokers gun so he can't really sit on a small lifelead too much and trade with it or force DS to get in ( assuming it's a small lifelead ofc ).
Quickfire trades are generally in jokers favour ( 6% vs 8% ) , but what i use quickfire in this mu is more about interrupting defensive teeths or slower cannisters ( wich he rarely uses anyways ) and to AA jump attempts wich works pretty well because Jokers low jump arc.
Upclose it's definately a good spot for joker , d2 range is huge enough to keep DS in check from jumping in , jokers air normals are faster , don't have height restrictions and have more active frames so he's winning more trades than DS , j2 / j3 are very hard to AA and when it does get AA it's mostly on a read , sword flip / d2 are not good enough to keep him out of the air.
Once you get a jump in it's frametrap city , DS backdash doesn't travel much far back/ mediocre recovery and it's very likely to get blown up by another j2 / j3 , Joker strings ( ala 323 ) leave him at advantage setting up d1s to check DS from hitting buttons ( tho 323 d1 can be whiff punished by walking back ) or get another jump in goin' , throws , lows and crowbar do a good job to get some decent damage into some setups.
In the corner it's definately not easy for DS as he has no easy mobility tool to get out and his wakeup Spin gets blown up by teeth setups , so i have to gamble on a Flip wich could get baited / pushblocked.
It's one of those matches that DS get to play his zoning game pretty well and can make Joker hesitate with guns to open him up with 50/50 , MB F3 works nicely vs jumpins and when Joker gets knocked down he has to block DS crossjump/non crossup setups into 50/50s.