It was widely known that Damon wasn't interested in doing another Bourne movie, but Hollywood being the soul sucking beast that it is, had to keep the franchise going. When Damon wouldn't come back to reprise the iconic character, studio heads began think how they can continue it without him. This time around Jeremy Renner is kicking tail, but the question is will it work.
Can you switch a main character in a franchise and still expect the people to love it the same? Can Jeremy Renner pull off a makeshift Jason Bourne? The studios were smart because they knew that they couldn't replace Damon with another A-list star, so they chose Renner. He's solid B-list and they surrounded him with A-listers like Rachel Weisz. My guess is that people will watch the movie expecting an action flick and that's what they'll get.
I don't think this will have the emotional investment that Damon's character had. Renner will run and jump through fiery hoops and bring in a respectable box office. It might even be enough to spring board him into A-list status. The movie won't do as well as the others because of the lack of Damon, but it will make a profit and insure another one or two more movies.