I haven't been to the Queen C. Islands, but we did do the inside passage on the way south from Alaska in 2006. By the time we got to BC we were pushing pretty hard and so didn't linger in the BC portion of the route. I'll offer a couple of thoughts of stopping points below.
There are several good cruising guides of this area. I'd recommend you research them and make the investment (they aren't cheap). We found the guides in this series very helpful:
FINE EDGE N.coast Bc at West Marine
You didn't mention the size of your boat or how fast you can move under power (you'll be using the engine a lot), so the estimates given below are based on +/- 6 knots SOG.
My guess is that from Vancouver to Port Hardy (good jump off place) is 4 days, maybe 3 if you push. Key here will be timing the transit of the rapids at or in the vicinity of Campbell River. North of the rapids there is plenty to see. I'd recommend the Broughtons -- Echo Bay is a good stop and you shouldn't miss Billy Proctor's museum there. Billy is a real character.
From the Boughtons to Port Hardy is a short run. Port Hardy is a good place to fill tanks and do final provisioning.
From Port Hardy northward we stopped at the following places (all a day's run on the engine).
Penrose Island - nicely protected anchorage in the inner pool.
Bella Bella - fuel availalbe, but not much else to brag about here.
Klemptu Passage -- protected anchroage at the south end of the passage
Fin Island -- (via Princess Royal Channel) nice anchorage. Across the bay is the FN village of Hartley Bay. You can tie to the town dock here and I believe fuel may be available, but I can't recall. There are fishing boats ported here, so my guess is they have fuel.
From Fin Island / Hartley Bay you have a choice -- either:
1/ continue on the inside-inside and run up the Greenville Channel (a long boring, but scenic, run up a narrow channel) where there are a couple of nice spots to stop on the eastern side. This is the route we took and we stopped twice in the channel between Fin Island and Prince Rupert. Prince Rupert is a nice town with full facilities.
2/ go SE to the Otter Channel to Nepean Sound, turn right and take the Principe Channel north to the top of Banks Island and from there cross the Hecate Straight.
3/ go SE to Otter Channel, cross Nepean Sound and take the Otter Passage north of Trutch Island (in the Estevan Group) into the Hecage Straight. This gives you a longer passge to the QC group, but you save several days motoring / sightseeing in the channels
The weather may dictate which route you choose. If it's forecast to be nasty in the Hecate Straight, you might find a few more days sightseeing the inside passage worthwhile.
Re timing -- we left Prince Rupert the first week in August. Weather was fine all the way to Puget Sound, where we arrived in late September. My guess is later in the season (July-August) might be slightly better than earlier.
5 weeks = 35 days. The day trips I've laid out above to get you to a jump off point on the east side of the Hecate Straight will consume 8-10 days pushing hard and averaging 6 knots. Assuming that on the way home to go direct from the QCs to the north tip of Vancouver Island (120 miles) you add another day or two. From the north end of Vancouver Is. to the San Juan de Fuca is ~ 200-220 miles, say 4-5 days pushing right along, and from there to Vancouver is another 2. So it's at least 8-10 days home from the QCs. That leaves two weeks for time in the QCs and various weather delays, pit stops, etc. along the way.
I tend to agree with Faster that 5 weeks is probably pushing it -- or to use William Buckley's phrase, a "race through paridise."
Another option might be to do it in two seasons -- season 1 to go from Vancouver to Prince Rupert, where you could winter the boat. Then season 2, take your time in the QCs and getting back to Vancouver. There might be other places to winter over, e.g. Bella Bella. You might check it out. It might be good to have researched a "bail out" spot where you could leave the boat if you had to for any reason.
Good luck and enjoy the trip.