It depends ...
Some tyre profiles are more sensitive to rim width than others. Dunlop, for example, says that their 180 slick works fine with up to a 6.25 inch wide rim. In the past, both Michelin and Dunlop have stated that a 5.5 inch wheel is suitable for 160 through 180 tyre widths. Different tyre manufacturers specify different rim widths for their tyres.
In general, you'll expect to use a 190 on a 6.25-in rim.