It seems that this is going to cost a fortune. Are there really no cheap flights from Toronto to Resolute Bay?
No, there really are no cheap flights from Toronto to Resolute Bay. This is a known problem, as small communities are hundreds of km from each other and thousands of km from any road. Long distance flights in often hazardous conditions with small aeroplanes. It means the local Inuit (unlike the extremely well-paid miners) are often unable to visit each other or to visit southern Canada, and inhabitants of southern Canada are unable to visit Nunavut. Although the article mainly focusses on food prices, this Huffington Post article from 2012 also notes:
Nunavut’s remote communities don’t have highway access, he says, and airline tickets don’t come cheap. A one-way to ticket between some Nunavut communities can cost up to $2,000, nevermind moving an entire family to a southern urban centre.
From Resolute Bay, you need at least two of such hops. I am not at all surprised that you find tickets for $5,000. I would not expect that you can get to Montréal for less than $3,000, one way.
For all practical purposes, visiting Nunavut as a budget traveller is impossible. Maybe you can hitch a ride of a freight supply ship, but there are no official ways through which this is possible, and you'll be on your way for weeks, if not months. If you try to get out by kayak, ski, or snowmobile, please make sure you are prepared for Arctic weather and Arctic wildlife. Good luck.