If you're interested in seeing the Canadian Rockies, then get to the Canadian Rockies, and don't spend any more time than you need to on the other places. If this is actually simply a "Western Canada Roadtrip", then it's certainly doable, but you'll be spending a lot of time in the car because the distance you're covering in the time you have is substantial. That said, some thoughts on each of your planned days:
Day 1: Vancouver - Hope - Kamloops - Sun Peaks
Not sure what you're looking for in Kamloops. No offense to those that live there, but it's not really scenic. But it does make a nice place to stop for gas and a meal. If you have to start in Vancouver, and are committed to driving from there, then you can get pretty close to the actual Rockies in one day if you simply drive straight to someplace like Blue River or Tête Jaune Cache. Then it's a relatively short drive the next day into Jasper (and if it were me, that's where I would spend most of my time.)
Day 2: Wells Gray provincial park - Spahats Creek - Clearwater River
None of those are technically in the Rockies. Might be an awesome place to go, and may be worth all 5 days, but if the classic Canadian Rockies are your goal, focus on being there.
Day 3: Jasper national park - Columbia Icefield - Athabasca Falls - Glacier Skywalk - Bow Lake - Moraine Lake - Lake Louise
You'll hit most of these on the way from Jasper to Banff, and unless you want to linger a long time in one spot, all of this can be done in a day, but it won't be relaxing...
Day 4: Banff Gondola - Banff town - Bow Falls - Emerald Lake
Again, based on your limited time, with so much else to see in the Rockies, I wouldn't spend a whole lot of time in Banff
Day 5: Okanagan - Kelowna - Vancouver
This area will be a bit of a let-down after being in the Rockies. Another idea would be to spend another day actually in the Rockies, then return the car in Calgary and fly back to Vancouver if that's where you need to end up.
Or, as another poster suggested, fly from Vancouver to Calgary, and rent a car from there, or better yet, start in Calgary, spend 4 days in the Rockies, then dead-head it down to Vancouver.
BTW, if you go to the Canadian National Parks website, you can register for a FREE pass that gets you into all Canadian National Parks for free for all of 2017. It's part of their 100th anniversary celebration. [edit: as noted below, it's actually the 150 year anniversary, which I really should have known, as I just received my pass in the mail the other day! : ) ]