The Dungeons of Ultima V are mostly less complicated than the ones of Ultima IV. However, instead of it being hard to pass through them, they now try to confuse the player and hide the way down, since the main reason to enter the dungeons is now to make it through to enter the Underworld. This solution shows the dungeons in an order in which they can be solved, starting with the easiest one.
Despise is by far the easiest dungeon, since only weak monsters inhabit it. Also it has no dungeon rooms at all, which makes things a lot easier. However, it makes up for this with being a confusing maze full of pit traps.
The easy solution for Despise is to just follow the directions on the map. Also be careful on level 8, since there is a horrible bomb trap hidden on that level. Later getting back to the surface is easy, since only one ladder leads up (compared to the many fake ladders leading down).
Covetous isn't that hairy of a dungeon, although after the weak Despise, it is the first real challenge in dungeon crawling. There is only one really difficult puzzle with a hard fight.
The Underworld below Covetous leads to the Shard of Hatred and is conncted to both, Covetous and Wrong. There is no real reason to visit the other dungeon once one is cleared, but of course it can be done for kicks.
The first five levels are straight forward (therefore three of them don't even have a map). The biggest problem is the sixth level. At first there seems to be no ladder down, until the puzzle is solved. The middle room has to be entered from the western room to reach the ladder, with a complicated puzzle to be solved. Also, this room and the middle room are infested with strong monsters. After that, the last two levels are easy. The way back is to just retrace the steps.
Wrong is a lot like Covetous, only with different kinds of monsters in it. However, it has two really nasty rooms.
The Underworld below Wrong leads to the Shard of Hatred and is conncted to both, Covetous and Wrong. There is no real reason to visit the other dungeon once one is cleared, but of course it can be done for kicks.
The whole dungeon is pretty straight forward, if you follow the directions of the map. The only annoyances beside random monsters are force fields and a pit trap on level 2. However, then comes level 8, with two very mean dungeon rooms that need to be cleared, before you can advance (careful, bomb traps!). The way back after this is trivial.
The problem in Deceit isn't getting down to level eight. It is getting to the Underworld and then getting back to the surface. It has a very difficult dungeon room-puzzle.
The Underworld below Deceit holds the Shard of Falsehood.
Right at the start, there are two routes: the conventional way, or the dishonest way. If the party is strong enough, use the dishonest way and a series of trap doors drops you right to level 8. search for a secret door and then move through the dungeon rooms until you reach the room shown on the screenshot. The trick is to take the torch and then trigger the walls and kill the enemies, until the way is clear.
Actually getting back to the surface is tricky. You have to follow the purple line on the map, beat a dungeon room and look out for pit traps, until you can exit the dungeon.
Destard actually isn't too difficult of a dungeon, at least until the final series of rooms, which are hardcore...
The Underworld below Destard holds Lord British's Amulet. Note that you can also enter it through the waterfall in Spiritwood, however, if no Gate Travel spell is available and you don't have any moongate stones with you, you can only exit through Destard.
Follow the route and solve the dungeon rooms on the way (they aren't hard). Once you reach level 8, the fun begins. The series of rooms blocking the exit is real hard. You can cheat if you are on your way to the Underworld by entering the southeastern room from the east and then exit south (which puts you into a wall square that you can exit west to get to the ladder). The honest way involves igniting a brazier and destroy Daemons then exit west to kill five Dragons before exiting south.
Note that getting back to the surface, if you've cheated, you have to face the Dragons, one of the hardest fights in the game.
Hythloth is surprisingly mild if you take the right route and don't get lost. Obviously to make up for this, the only dungeon room you need to enter is a very hard battle.
First climb down right to level 7, ignoring everything else. Then find the secet door on the norther wall and follow the path on the map, until you must search for another door on the eastern wall. The ladder leads to the corridor to the dungeon room with the ladder down. It is infested with Daemons. After they are killed, the way back is easy.
Shame might look hard at first, but like Hythloth, the trick is to take the right route and withstand the temptations on the way.
The Underworld beneath Shame is the only way to reach Dungeon Doom, the goal of the game.
The first room looks more difficult than it is, follow the instructions on the screenshot, which walls to push (you can climb the rocks). Now take the easternmost ladder on the first level, which leads right to level 7. There, take the ladder south of you to reach level 8. Beat the room, then walk to the southern room and beat it as well. Exit to the east, find the secret door and climb down the ladder.
Needless to say you don't need to return to this dungeon for the surface.