The useful rule-of-thumb for minimum stencil aperture size related to paste type is known as "the five-ball rule." It is the worst-case number of paste sphere diameters that will fit across a stencil aperture.

For a type 4 paste, the largest sphere size is 38um and so the worst-case stencil aperture width is 190um (~7.5mil) and anything less than this may give paste printing and release problems.

You don't need to go to a type 5 paste if your designs are hitting this limit, as many paste suppliers now provide a "type 4.5" paste where the larger sphere sizes in type 4 are sieved out, with the maximum then only 32um which means you can have a 160um (~6.5 mil) stencil aperture providing the foil thickness needed doesn't break the area and aperture ratio rules.

If you need type 5 then you probably have features that need apertures as small as 125um (~5 mil) wide.

In practice you can get away with smaller aperture widths since you would rarely encounter the worst-case but your process window and repeatability suffers if you don't take this into account.