A modest rise in resting heart rate is common with GLP-1 drugs. I have not seen reports linking them directly to sleep trouble, but if someone is already close to the edge it could matter. Separately, you moved from 2.5 mg to 5 mg fairly fast. Was the lower dose no longer effective? Did you test 3 mg or 4 mg first?
I began tirzepatide at 2.5 mg weekly last August and have increased to a single 5 mg weekly shot. As an older person with a prior TURP I already wake two or three times a night to urinate. Before this medication I usually fell right back asleep, but lately most nights I struggle to return to sleep after getting up. I wonder if tirz changes sleep for others on it and whether anyone has ideas that might help. I already keep the room dark, avoid screens in bed, and wind down beforehand, yet the trouble has clearly increased since starting the shots.