What components have a MSL of 5 and 6?
The industry-standard JEDEC MSL values imply a component's "floor life" (time spent in storage bin before being mounted on a PCB) at a specified temperature and relative humidity, as well as standard and accelerated soak requirements; i.e. how long to bake at what temperature and what relative humidity, so that the part can be safely mounted in a reflow oven.

As an example of a highly moisture-sensitive component: nearly a decade ago, back in 2008, the Maxim Integrated MAX7320 Evaluation Kit used Optek OVSASBC2R8, a PLCC packaged surface-mount LED. Our first prototypes had a lot of problems with "popcorn" defects, where moisture inside the package would cause the LED to burst during reflow, like a kernel of popcorn. The LED datasheet lacked any useful information about moisture sensitivity, other than a little blue circle-slash icon with little water drops. We next instructed our contract manufacturer to try baking the parts at 60°C prior to assembly, but still got unacceptably low yields on our next run of prototype boards. When I pressed the Manufacturer's Representative for details, especially what exact JEDEC MSL rating was required, they admitted the device's MSL was 5a (even worse than MSL 5), requiring mounting within 24 hours of opening the bag, otherwise bake 24 hours at 80°C to dry them out before mounting.

For early surface-mount LEDs this was a difficult problem, because unlike most ICs where the integrated circuit chip is coated on all sides with opaque epoxy, the LED chip needs some optical lens components, supported by an opaque plastic enclosure. This was kind of a new problem back then, and the packaging engineers didn't have a good way to deal with it. There were interior spaces within the package, where moisture was unintentionally trapped, which then exploded out as steam when the component entered the reflow oven.

Any level of moisture absorption is undesirable in a typical epoxy coated IC package, because it can cause popcorn defects at assembly. Packaging engineers try to avoid having a high MSL for this reason. Most likely you're not going to find any modern devices that still requre MSL 5. Surface-mount assembly is a requirement for any modern high volume production line, and high MSL parts are just defects waiting to happen. So over the past decade these parts will have been phased out and replaced by more reliable parts, either by improvements in the design of the package, or by complete redesign.