score:3
5 weeks is plenty for that trip, including Rinjani. Several years ago I did a trip from Maumere to the Gili islands west of Lombok in 4 weeks, by (private, small tour group) bus and boat, 4 weeks of slow travel over the islands. If you plan to use internal flights to bypass some islands and most boat travel, you've plenty of times to extend the trip further west in 5 weeks.
The boat tour to and around Komodo and Rinca will take 2-3 days (depending on the exact itinerary of course), half a day out, afternoon on Komodo, sleep on board, short crossing to Rinca, visit there, and back to LBJ for example. While interesting there's not all that much to see or do in the national park, so that's plenty of time for most people.
DPS-LBJ-JOG-LBJ is certainly an option.
Upvote:0
There are no non-stop flights between LBJ and JOG as you have discovered. There are from Jakarta, but that is no better than connecting in Denpasar.
If the 7 hour layovers sound undesireable, perhaps consider inserting a Bali stay between the adventures. Arrive in Bali do something, fly east to adventure one, fly back to Bali explore central Bali, fly west to adventure two, fly back explore the rest of Bali.