My recommendations would depend on what your players enjoy.
Regarding some of the adventures others have suggested.
WHAT YOU SHOULDN'T RUN
Waterdeep: Dragon Heist - I am running this now and can't wait for it to end. In my opinion this is among the worst - possibly
the worst - official 5E adventure. It's an unfinished product. Chapter 2 in particular is a nightmare for new DMs. For an encore, it covers exactly the same levels (1-5) as Lost Mine of Phandelver, so if you plan to continue with your 5th level characters you'd need to re-work everything. Honestly, you'd have to re-work everything anyway because it's really bad.
Storm King's Thunder - I know this looks good on paper. There is an obvious on-ramp at level 5. It's in the same general region as Lost Mine. But that's where the virtues end. You're already level 5 so you'll mercifully skip the irrelevant levels 1-5 prologue part. Your adventure will begin in a city on the Sword Coast. As a pointless gimmick, in the first session your players will play NPCs assigned to them instead of their own characters as they defend a city from giants. You might think this is smart because then your players will develop an attachment to either these NPCs or the city they are defending. Nope! Your players talk to the NPCs once and then leave the city forever. Then for the next two levels of play you are given 50 pages of thumbnail descriptions of the Sword Coast and told to make up your own adventures (this is not the sort of thing I buy a $50 hardcover for). Finally, around level 7, the adventure (billed as covering levels 1-10) starts. From that point forward it's...okay. Except that the adventure does everything possible to conceal its pointlessly complicated plot from the players - in fact, they may finish it without really understanding what happened.
WHAT YOU MIGHT WANT TO RUN
Waterdeep: Dungeon of the Mad Mage - If your group really likes dungeons and combat, look no further. It even starts at level 5. To flesh it out and add some much-needed depth and connectivity, grab Wyatt Trull's Dungeon of the Mad Mage Companion from DMsGuild:
https://www.dmsguild.com/product/311108/DotMM-Companion-Complete-Edition
Dragon of Icespire Peak - But only if you really want more of the same. It's more Phandalin, more quests (even simpler than Lost Mine). Covers levels 1-6 so again you'd have to re-work a lot of encounters for higher levels, or just skip to the level 5&6 stuff. The free follow-up adventures on DNDBeyond are a mixed bag. Storm Lord's Wrath is pretty great - in some ways better than Dragon of Icespire Peak - but the following two are quite bad.
Curse of Strahd - Still the strongest 5E adventure and actually a great second adventure to run. It's considerably more complicated than Lost Mine but still WAY simpler and limited in scope than most of the other 5E hardcovers. But not the right choice if your group isn't story-focused. Starting this at level 5 is fine, just don't use Death House.