From St. John to island hop requires a lot of backtracking and work unless you stick to Virgin Islands. With only 5 days you'll loose quite a bit in travel. Most require either a connection to Miami, or Puerto Rico. Yu tagged Anguilla, that requires either additional flight through St. Martin with a ferry or a very expensive flight from PR.

Anguilla has amazing restaurants, gorgeous beaches, but no real snorkeling scuba, it's about relaxing on upscale gorgeous beaches. St Martin has excellent restaurants, it's fun an active, but no real snorkel and beaches not as nice as where you're coming from or Anguilla.

So my a dive:

Stick to Virgin Islands. There are many to hop around, even with 5 days you won't be able to do half, and each is unique and gorgeous and offers something different.

The best combination is with Virgin Gorda. Stunning beaches, the Baths are amazing with big boulders in the water. You can also day trip sail to Jost Van Dyke which has a gorgeous strand of a beach. Tortola is colorful, including the shopping. The beach bars are really cool, for example Pussers at Marina Cay is colorful and on it's own island. You may want to consider staying at the new gorgeous Scrub Island, and day trip to VG and JVD.

Yu really need to stick to Virgin Islands, not just because of time constraints, but because they have a lot to offer and have what you're looking for.

Many think the Caribbean islands are all close and easy to get around. Like Europe where you can see 3 countries in a week. This is far from true, there are many open waters with no ferry systems, and air requires much back tracking and most times even overnights to meet the flight schedules. Many islands themselves, such as VI have tons of islands in the grouping.

Stay in Virgin Islands the whole time. It's has what you're looking for, and you still get to island hop.