I am wrapping up my Lost Mines of Phandelver adventure and I have a party of 4 adventurers  and they are all level 5 but are close to level 6.  LMoP was the first adventure I ever DM'd and it has taken us about 12 sessions (3-4 hours each) to finish the adventure.  I've added at least 20 hours of custom stuff to the adventure so I like having a rough template that an adventure can provide, but my players and I both like adding quite a bit of custom stuff to the adventures.

The players want to continue their characters onto a new adventure so I'm trying to find a new adventure that would be good for a bunch of level 5 or 6 players.   Most of the adventures I have come across seem to have significant sections dedicated to leveling up from 1 - 5.  Is there anything that is recommended for some players that are already level 5 or higher?  The only thing I don't want, is a pure dungeon crawl adventure like Tomb of Annihilation.  My players seem to really enjoy changes in environment and getting to travel from time to time.  Any suggestions? 

The players are pretty casual I would only consider 1 of them to be an intermediate player.

Get them to Waterdeep and then run Dungeon of the Mad Mage. Let them curb-stomp the first few floors and let them feel strong before they get deep enough for the dungeon to catch up and become very....very dangerous.

Edit: To avoid letting it feel like a pure dungeon crawl, let them leave and come back, exploring Waterdeep in between and making connections with various NPCs around the city. Also remember that the dungeon is monitored and stocked by a crazy wizard, so don't let cleared floors stay empty and also keep a short note sheet for each floor detailing how any monsters the party leaves alive or makes friends with influence and spread across the floor. Maybe the goblins they choose not to kill begin to worship the party and veg them to help fend off newly added monsters on their floor. Maybe some drow from one floor have beef with duergar from another and pay the party to pick a fight.....etc 

There isn't much that starts at level 5.

Dungeon of the Mad Mage starts there...but that is a dungeon crawl.

Light of Xaryxes starts there...but that's sold int he Spelljammer set, and that's expensive to buy (and is widely agreed to be a poor deal). The adventure is really short too (L5-8).

You could skip the early parts of Rime of the Frostmaiden, but to be honest... that's skipping the good part of the adventure. The initial few chapters are really good, but at around level 7 or so it switches to old style dungeon crawl and we're just finishing it for the sake of finishing it.

I believe Storm King's Thunder has an Introductory stage you can skip and start at L5, but I've not played it yet, so I'm unsure of how good it actually is.

You could try Dragon of Icespire Peak. Either curtail their progression until they catch up or just skip the first few quests - they're not important anyway. You could then top up with the Beyond Icespire Peak Trilogy to go to L13.

Vecna: Eve of Ruin starts at L10 and goes to L20 but you have to get to L10.

The problem is that the game gets unbalanced after a while,.so adventures tend to end at around L10-13 to avoid having to deal with that. To avoid short adventures then, they mostly start at L1. Anthologies are the main option for starting at later levels, but their anthology nature means that they're largely dungeon crawls.

You might be able to find something on DMsGuild or DriveThruRPG.

Quote from jeffloeb1976 >>

I am wrapping up my Lost Mines of Phandelver adventure and I have a party of 4 adventurers  and they are all level 5 but are close to level 6.  LMoP was the first adventure I ever DM'd and it has taken us about 12 sessions (3-4 hours each) to finish the adventure.  I've added at least 20 hours of custom stuff to the adventure so I like having a rough template that an adventure can provide, but my players and I both like adding quite a bit of custom stuff to the adventures.

The players want to continue their characters onto a new adventure so I'm trying to find a new adventure that would be good for a bunch of level 5 or 6 players.   Most of the adventures I have come across seem to have significant sections dedicated to leveling up from 1 - 5.  Is there anything that is recommended for some players that are already level 5 or higher?  The only thing I don't want, is a pure dungeon crawl adventure like Tomb of Annihilation.  My players seem to really enjoy changes in environment and getting to travel from time to time.  Any suggestions? 

The players are pretty casual I would only consider 1 of them to be an intermediate player.

You could run some of the one-off adventures from Candlekeep Mysteries, Keys From the Golden Vault etc. rather than a lengthy campaign, if the players enjoy different challenges and locales