Sorry for the late response, but there is no problem using a slightly larger reel. It might be a tad big, but it's not a particularly heavy reel. If I were fishing a 5/6 wt rod, I would probably buy a new reel (ok, I use almost any excuse to buy a new reel) but just try your reel for a while and if you don't like it, get a new one.
Just take of the existing line in a nice coil and put it in a ziplock bag (for when you want to use a 10wt again) and put an 8wt line on the existing backing. It won't fill the reel quite as much, but it will work fine. Fish it for a season and if it is too heavy, then you can buy a new one.
Trying to use a smaller reel with a heavier line can cause problems because there often just isn't enough room on the reel for the larger line (with backing).