Hey! Sounds like an interesting way to spend some time in the mountains so why not.
https://where2walk.co.uk/home/walking-challenges/bob-graham-round/ is probably a good place to start and gives more of an overview.
One thing I'd consider is how 'beholden' are you to the original route and how much would you want to go slightly away from it to get a more interesting/scenic route. If you're keen to stick to the original, absolutely fine, but be aware there may be accommodation options/route alternatives elsewhere.
In terms of places worth stopping for accommodation, 4-5 days is pretty leisurely so you can afford to spend some time in each place in between walking. Keswick and going clockwise is probably the easiest route (relatively simple first day and Scales/Threlkeld has a decent pub to stop at) then decide whether you want to turn Day 2 (Clough Head and due south towards Grasmere) into a one day epic or take your time and break it up. The Lodge in the Vale is a good stop about half way down and does a superb 'hikers breakfast' (I remember eating an absolute load of food when I was skiing there last), though there are pubs north of Grasmere on your route (Travelers Rest I believe but look it up) if you'd prefer to keep your route shorter. I'm not a fan of the Dunmail route up Steel Fell as it's always fkin soaking wet whenever I'm there so my personal preference would be to spend a night near in Grasmere and head up Helm Crag for a more characterful route up the Easedale valley - however that would take you technically 'off route'.
From Grasmere you're heading towards Wasdale Head and if you're having a leisurely route you might look for accommodation in the Langdale area. At this point a lot depends on your pace and confidence in the mountains - as you've got Langdale, Wasdale, Rosthwaite and Keswick/Portinscale/Brainwaite as the 3 night stops respectively. Old Dungeon Ghyll (or somewhere else in upper Langdale) to Wasdale Head is quite a decent hill day out which is why I'd be inclined to break up the route over the eastern fells in to two days, not least because it's one of my favourite routes and deserves a leisurely pace to savour it but because it'll leave you fresher to enjoy the slow pull up towards Bow Fell and lets you enjoy some of the best views in the area on this day.
From Wasdale Head, the Honister Pass is likely a better place to stop for that day's exploits rather than pushing on to Rosthwaite unless you're planning to give yourself a bit of a rest and explore the lower Borrowdale area. I quite like Glaramara (the hotel) as they've been sensible with Covid security, have a cozy bar and are well set up for hikers without being as austere as some hostels can be - but this would represent a commitment to a bit more up/down and you'd need the legs to do it. Last day over the Derwent Fells should be quite simple if you've made it that far and Robinson will give you some variety in the descent.