Since you want to fly back from Mandalay, it has to be your last stop, so that limits your choices in your city itinerary. So Yangon-Inle-bagan-mandalay or yangon-bagan-inle-mandalay are both fine.
Do you intend to take ground transport or fly? I suggest flying, as ground transport is notoriously slow.
If you have 3 extra days, try a Mandalay-Maymyo(aka Pyin U Lwin)-Kyaukme (pronounced chao-mei, sounds like strawberries in Mandarin) side trip.
I took a shared taxi from Mandalay to Maymyo, spent 1 night there, then took a train to Kyaukme. On the way between Maymyo and Kyaukme (ticket price USD 2 for the 5-6 hour journey), the train will travel over the fabulous Gokteik Bridge, at one time the highest steel train bridge in the world. Sit on the left side to see the bridge best. Totally worth the train ride.
Maymyo is a small British mountain town like Malaysia's Fraser Hill, while Kyaukme itself is also a small mountain town that's popular for mountain trekking. It's also a good way to relax and unwind in the cool mountain air and just do nothing.
At the time I went, there was only 1 approved tourist hotel (around USD30 per night) in Kyaukme, so book in advance if you intend to go. I can also hook you up with a good English/Mandarin-speaking local guide for trekking if you want. I did the return journey from Kyaukme to Mandalay by shared cab, which was much quicker ( 2+ hours).