Fifth wheels should be very, very stable and fishtailing or sway is most unusual. Sounds like there is inadequate weight on the kingpin (hitch). On a fifth wheel, at least 11% and as much as 18% of the total trailer weight should rest on the hitch for proper handling. The first step is to get your rig weighed, axle by axle, to determine total weight and how the load is distributed.
Do you usually travel with water in any of the tanks (fresh, gray or black)? One or more of your tanks may be behond the trailer axles and water (which is very heavy) maybe causing an imbalance.
Your half ton Chevy may be a bit wimpy too - half tons are made to ride and handle more like passenger cars and sometimes some stiffening in the rear will help keep heavy tows in place. The addition of air bag assist (Firestone Ride Right or similar) sometimes helps. I wouldn't jump into that, though, without the weigh-in and some further discussion.