Five days on Mendip should be enough to do most stuff!
How about....?
1 day: GB thorough explore everywhere & then "do" Tynings Barrow Swallet
1 day: Swildon's Hole round trip via 4 detour & perhaps check out Vicarage Passage, NW Stream Passage and Black Hole series on way out (or do Swynne-Puke pull through above Shatter Pot on your approach to Swildon's 4?)
1 day: St. Cuthbert's Swallet comprehensive route taking in September series, to sump 2, Rocky Boulder series and maybe Maypole series?
1 day: Eastwater Cavern - twin verticals route/13 pots or just go as far as you can?...
1 day: Longwood August in morning and Manor Farm Swallet in afternoon to the bitter end/bottom of both.
Also perhaps check out SRT optional extras: Rhino Rift (multi-pitch pot), Thrupe Lane Swallet high ATLAS route (60m pitch).
... Mind you, you'll need to be pretty damn fit to do all that without a break! - also you'll need to organise a leader for Cuthbert's and keys/permits for GB, Longwood, Rhino Rift. Keys required for Tynings Barrow Swallet (I've got contact details if required) and you need to make goodwill payments for Swildon's Hole, Eastwater Cavern, & Manor Farm Swallet.
Also worth a look are...: Stoke Lane Slocker, Shatter Cave, Hunters Lodge Sink, hmmmm.... anyone else got any ideas?....