Well, if I told you about any little known gems, then they wouldn't be little known any more, would they?
Just kidding. I'll do my best to help. Unfortunately, there are a billion things to do in the park, and you'll never get to them all in 5 days. Despite the crowds, I would spend at least one day in Yosemite Valley just to see it--it's a tourist mecca for a reason. The sights are amazing. However, I would make it either Tuesday or Wednesday because those days are a little less busy.
It's very hard to find secluded places without backpacking or doing very long day hikes. There are only a few roads in the park, so they become pretty crowded. 94% of the park is designated wilderness area (which means no cars, bikes, or anything with an engine).
Basically, this means that you'll need to go hiking to find seclusion. I'll start from the South end and head north.
In Wawona, there's a trail called Alder Creek. The first section of the trail is pretty dry and hot with little water. However, once you reach the junction with Mosquito Creek (which is a shortcut and another way in), it flattens out and becomes more covered with trees. After roughly 6 miles, you'll get to Alder Creek falls, and you can cool off in the creek. I highly doubt that you would see anyone out in this area.
There's also the Mariposa Grove of Giant Sequoias. It is crowded, but only if you stick to the lower half of the Grove. The higher up you get, the less crowded it is. If you get up above the museum, there are hardly any other people.
Moving north, you can get to the Glacier Point area of the park. You can do a day hike out to Lake Ostrander, which is a 12 mi. round trip hike. It's a beautiful lake. You will see a few people out there, but if you head to the eastern side of the lake (to the left when you get there), you'll escape most of the people (which would only be a few--probably less than a dozen).
Drive out to Washburn Point or Glacier Point while you're there. It's very crowded, but the views are amazing. You don't have to spend a lot of time there, but it's worth the crowds to be out there.
In Yosemite Valley.... well, like I said, spend a day there (since it is your first time, it has to be done), but be prepared for crowds. There aren't any locations in the Valley that don't have crowds (unless you live there and know the area, which I do not).
Moving further up, you'll get into Crane Flat and the Big Oak Flat areas. There are a few good secluded places in the area, namely the Merced and Tuolumne Groves of Giant Sequoias. There will probably be a couple dozen people in these groves, but compare that to the Mariposa Grove, where you'll see hundreds of people in the lower area.
Further up the Tioga Road (Highway 120 East), you'll run across a few trails. If you start from the Porcupine Flat campground, you can hike out to North Dome (~10 mi. Round Trip), which is a great place to see Yosemite Valley from a fairly secluded location.
In Tuolumne Meadows... well, it's the second most popular area of the park. There are very few places to get away to. You could hike up Mount Dana (about 7 miles RT), which is right on the edge of the park, but that hike doesn't have a designated trail. A shorter hike is the Gaylor Lakes area, which is 2 miles RT, but it has more people.
In short, the best thing to do would be to ask a Ranger when you get into the park. Take these suggestions into consideration, but listen to what the Rangers say about conditions. They'll be able to give you the latest information on where other people are going, as well as trail conditions and road information. They can help you find any of the trails I've mentioned, as well as others I haven't. Enjoy your stay in Yosemite!
