I am a huge Fabled Lands fan and have thought about this A LOT.
You could come at this in one of two ways - using the world (at least as much as we know) for your own stories or trying to stick to some of the quests and storylines in the original books. I would personally go with a mix by largely letting the characters explore the world for their own ends and cherry-picking some of my favourite storylines from the books to include (e.g. Lauria, the Sokaran Civil War, Nyelm Starhand...)
The second consideration is how well the books and the world fit D&D 5E. In general, the fit is very good. It is much closer to DnD than Lord of the Rings, for example.
FL has the same "syntax" as DnD - there are classes, characters go on quests and loot is important. There are a pantheon of gods with recognisable domains. The land is populated by monsters and some areas are more dangerous than others. There isn't a big battle between good and evil, it's mainly just people being people.
I can think of two big differences. One is easily surmountable, the other one less-so.
1) As others may have commented, the books have an arbitrary and "swingy" level of difficulty. This is against the ethos of DnD 5e. But it should be trivial to correct as a DM because you choose the difficulties and encounters. If I did want to preserve this feeling of harshness, I would try adapting it to Savage Worlds, not DnD.
2) Fabled Lands is a human world. It would be difficult to play a non-human. Many of the standard DnD races are simply not present. There are other races (trow, mannekyn, merfolk...), but these are presented as strange and wonderful. They don't have kingdoms, politics etc - they are "others". I think this is a consistent theme across Dave Morris' works, where he wants to evoke folklore and myth more than Tolkien.
But it is a problem because it goes against the design and flavour of DnD 5e, which seems to encourage one to play a fantastical race that is balanced with humans. You would have to either change the world OR tell players they could only be humans OR create your own races. All of these are a lot of work and might affect game balance as well as theme.
Finally, there IS an official Fabled Lands RPG, published by Greywind Games. Don't know how easy it is to find in America. I have not played it, but... I have to say that it doesn't look very good! It essentially expands on the FL rules system and I think it would keep all the flaws of the books' rules. The production is nothing special and it isn't supported by any adventures. I don't see a benefit to using it over DnD or Savage Worlds.
