Lots to see in 5 days. You are staying at Fishing Bridge, so I would start with the South part of the Grand Loop road first. Simply because it contains the Old Faithful Geyser Basin. Lots of features to see there. It can involve a lot of walking. The West side of the South Loop has numerous features also. And there are some on the East side. If you have not obtained a map the park go to the YNP Website and get one. Also search the internet for the YNP Newspaper. The Summer version should be printed shortly. It will contain road information, closures, construction, etc. Plus other general stuff. Lots of Picnic areas along the loop road. Bathrooms also. Car travel is slow. Do not assume you can average the 45pmh limit. To many stops and interruptions along the way. Can’t comment about trails and fishing. I supect you will be tired at the end of the day just by walking the various thermal features. Other folks at the various stores and the campground will tell you about bear sightings and /or other animal issues. Talk to people. I consider the Old Faithfail area, the Canyon area, the Mammoth area and the Norris Geyser area as “must sees”. There are many other area. Pick and choice as you see how your time is going. If you have never been to the Grand Tetons you should exit YNP to the south. I understand time may be an issue for you.
2003 Newmar Scottsdale, SDCA 3257, 8.1 Vortec