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I don't have a reference that lists the Sharps rifle, but the Ruger (no1 & no3) as well as the Marlin 1895 all use a 1-20" rifling twist. Probably so does your Sharps.

The easy way to check is to use a snug fitting patch (so it turns in the rifling), and run it down the bore, watching until you get one complete turn. Mark the rod, and then remove it and measure the length to the full turn mark. That will give you the one turn in X inches rifling twist.

If your Sharps has a 1-20, then expect the same potential from the Ruger, when it comes to handling bullets of 500gr. An inch or two faster or slower doesn't mean that the Ruger will not handle those bullets well, just that it might behave a little differently. For instance, if your Sharps has a 1-22" barrel, vs the Ruger 1-20, you might get similar results with 500gr bullets, but you might not. Probably you will.

There are several calibers where a range of rifling twist rates will perform satisfactorily with the normal range of bullets, but some twists will not do well with certain weights. How large this range is, depends on which bullets (and calibers) you are looking at.

.30 caliber rifles perform well with twists ranging from 1-9 to 1-12. Most common is 1-10" or 1-12". .22 centerfires are more...specific, depending on the preferred bullet to be used. .22Hornets, shooting light 40-45gr bullets (standard) are 1-16". .222Rem, .22-250, etc., where bullets are expected to be in the 50-55gr range use 1-12 or more commonly 1-14" twists.

.223 rifles use a variety of twists, 1-12 or 1-14 used in rifles intended for varmint shooting with 50-60gr bullets, faster twists of 1-10, are used in some (Mini 14), and specialty rifles (AR variants mostly) intended to use the newer heavier (and longer) 77gr, 80, or even 90gr bullets use 1-9, 1-8 or even 1-7" twists.m There is no free lunch, however, and twist rates at the extreme ends of the ranges do not do well with bullets from the other end of the range.

This is more important in smaller bores, as the ratio between bullet weight and bullet length is more pronounced than it is in larger calibers. In .45 caliber, the difference in bullet length between a 400 and a 500gr bullet is not as much, proportionally, as the difference between a 45gr and a 77gr .22 cal bullet. A twist that works well to stabilize a 400gr .45 will do fine with a 500gr .45, but a twist that does well with a 50gr .22 seldom does well with am 80gr bullet. For example, I have a .22-250 that is 3/4" with 53gr match bullets, but only 1.5" or larger with the Sierra 63gr semispitzer, because the 1-14" twist is border line for the longer heavier bullets. .22 are picky.

.45s are much more ..tolerant in that regard. I believe that the Ruger No1 (or no3) will do acceptably well with 500gr bullets, and if not (possible, but unlikely), it will be something else about the rifle other than the twist rate that causes it.