There aren't many barriers!
Many adventures published during the older editions of D&D are still useful for DMs of the fifth edition, mainly because the overall base of monsters and treasures across editions is quite similar, while the main aspect of the adventures – the plot – is usually untied to the rules of its original edition.
I am, right now, DMing some D&D 4E modules for my group, the H1-H2-H3 trilogy: Keep on the Shadowfell, Thunderspire Labyrinth, and Pyramid of Shadows. The adaptations I usually have to do are balancing the encounters and choosing the players rewards. I'm following the guidelines of the Dungeon Master's Guide and Xanathar's Guide to Everything for rewards and I haven't run into any trouble regarding converting these adventures.
Wizards of the Coast has an official conversion document that can help you convert older modules, rules-wise.
One important thing to notice is that White Plume Mountain is already officially converted to 5E. It was published in Tales of the Yawning Portal, a book that features a good number of adventures from older editions adapted to run in D&D 5E, including The Sunless Citadel, The Forge of Fury, Against the Giants and some others classic modules.
The Ghosts of Saltmarsh campaign, released in May 2019, also features conversions of some modules from older editions, this time, sea/pirate-based adventures.