Top five that no one has heard about? Tall order!

But here are a few you might not have heard about, in no particular order. These aren't the five most significant or anything, but they're cool, and important for various reasons.

Sutton Hoo was not a wreck, but an Anglo-Saxon burial from the 7th century. There're really beautiful artifacts from the site, including a helmet that's become iconic.

Blackfriar I is a 2nd century ship found in London. It's neat because it may show frame-first construction of a native style, rather than the mortise-and-tenon construction typical of the Romans who ran the place. Mortise and tenon means that the planks were held together along the edge with pegs and slots, rather than by internal frames. In any case, it's definitely different than what was going on in the Mediterranean.

Serce Limani, an 11th century ship which sank in Turkey, is also important. It doesn't have any mortise and tenon joints at all, and is one of the early examples of naval architecture. It was built in some sort of units, and the frames were spaced in multiples of that. The keel and posts were built first, and then a pair of midship frames. The shipbuilder would have added a couple more frames, and then put planking on the bottom. Once the bottom of the hull was described, the shape of the rest of the ship could be determined, and it was finished. The ship was carrying glass, which was likely some sort of glass-recycling effort. It would have been steered with a pair of rudders hung from the quarters.

La Belle was a small French ship which sank in 1686 in Texas. This was an early attempt by the French to colonize the Mississippi river, but a poor map misled them and they wound up in Texas. Combinations of poor decisions, ineffective leadership, bad luck, and hostile natives led to their colony getting into some trouble. Then their last remaining ship, La Belle, sank, and that was the end. Their leader, La Salle, tried to convince people to walk to the French settlement at Quebec with him, but they wound up killing him. A couple guys did walk to Quebec, and survived. In 1995, the ship was discovered, mostly intact on the bay floor. It was raised whole, and while the final publication isn't out just yet, there are a multitude of artifacts aboard, including most of what you'd need to start a colony. That ship was built with doubled internal frames, which is a construction method usually connected with the 18th century. It was also a "ship kit" that had all of its frames numbered, so it could be assembled in the new world. Because of space issues, the French wound up building it in France and sailing it across to the new world itself. Lots of artifacts, new shipbuilding techniques, and the first European permanent settlement in Texas make this one a big deal.

The fifth is a bit of a challenge. I want to go with Vasa or Kyrenia, but those are pretty well known. Instead, I think I'll break with the spirit of the question a little and go with a type of wreck - the ships buried under cities. One of those, the Ronson ship, was found in Manhattan, what's now several blocks from the water. It was most probably a mid-18th century ship, and only the bow was recovered. Another example of this sort of thing is Niantic, a wreck found just next to the Transamerica Pyramid building in San Francisco. It was a whaling ship that brought gold rush folks to California. Like so many others, its crew abandoned it for prospecting when it got there, so it was turned into a floating warehouse. A doorway was cut in the side, and it was built on, and built on, turning into more of a building all the time. Finally, fire and landfill took their toll, and Niantic was buried... only to be rediscovered in the late 70s. I chose this last pair of examples to illustrate that shipwrecks sometimes lie under our feet as well as under the waves - steamboats frequently wound up miles from the rivers they sailed on, due to shifting rivers.

This was a long post, but I'm glad someone finally asked something in my wheelhouse!