Welcome to iMore! Two thoughts...
1. The display on the 6s Plus is going to show more imperfections in the photos than the smaller, lesser resolution screen of your 5. Furthermore, the iPhone 5 took good photos but the 6s Plus takes AMAZING photos. If you're comparing photos taken by each phone side by side or one right after another anything taken on the 5 is going to look fuzzy.
2. Do you have iCloud Photo Library enabled on your 6s Plus? It's under Settings > iCloud > Photos. If it's toggled ON and you have "optimize iPhone storage" checked on it could just be that you're seeing optimized versions on your phone which tend to look fuzzy. If you give it a few seconds your phone download the full resolution version that looks a lot better. I'm just guessing here. It could or could not be the issue.