My first question was the same as WB's. You can't play 18 holes of golf well with one club. I do a lot of nymphing with a 4wt, but 5 is better all around, simply bc the more massive line and added power in the rod will manhandle more weight. By winter, I'm using a 6wt where in summer I used a 4.
But, even with the right line, there is often an adjustment in casting needed. As Louis' suggested, the "Oval Cast" is the way to go (named by Lee Wulff). With it, you can pitch more terminal weight (safely and accurately) per line weight. It also can be embellished at the end for tuck casts and accurate pile casts that help get your weighted nymph down before the leader engages with it.
Most simply, oval casting is bringing the line under the rod on the back-cast, and then over on the fore. Depending on weight, you probably won't be able to put a lot of line in the air like you can with an unweighted fly. So work with less line in the air, oval cast, then shoot what you need. You can move a fair amount of weight, safely and accurately, this way.
The backcast is a strong upward thrust, waiting for the weight to load the rod, then you throw forward and "over the top" of the rod aiming high, and letting the weight carry the rest of the cast out.
I had an article in the Jan/Feb 2003 American Angler about using leadcore heads (incorporated into the leader) called "Core Values" that highlighted the oval cast. I use leadcore heads for streamers and wets on both strong trout streams as well as steelhead waters (where one tends to hear the most about sinking heads). The oval cast, and shooting line, is the ticket. Here's a sketch of the oval cast I sent in with the article for their artist to use:
I also have the illustration the artist did but I'm not sure if it's kosher to post it.