The general principle of conversion is to keep the general sense of the original, but be prepared to throw out all the numbers and game mechanics which will not apply in the new edition.
Many things can be used as-is. Dungeon maps, overland maps, plot hooks, general storylines, and so on, can be used with little or no changes.
When it comes to monsters, you basically need to create new encounters based on 5th edition monsters and encounter building guidelines, using the 4th edition encounters as inspiration. 4th edition encounters are too different: 5th edition has no equivalents of elites or minions, and its monsters may be different level to their 4e counterparts.
Give out treasure based on the D&D 5th edition expectations of gold and items, rather than the 4th edition standards. 4th edition had the assumption that you could buy items with gold, and that edition's treasure system was different in general. You probably want to insert similar items to the original where possible.
In general, you want to adhere to 5th edition sensibilities and design, forcing the 4e material to change to adapt to that, rather than the other way around.
Another thing to note is that 4th edition goes up to level 30, whereas 5th caps out at level 20. It's somewhat arbitrary how to translate the level difference, and you'll want to adapt the adventure to your party's level anyway.
Most of settings books can be used without modification. They're full of rules-neutral material like maps, history, politics and setting lore. All the basic concepts are still there, like fighters, wizards, characters who increase in level, and so on.
Some of the free 5th edition Unearthed Arcana material includes statistics for setting-specific material, such as the warforged and shifter races for Eberron.
Remember, also, that it's your world, and you're free to invent new things and fill in the blanks as you wish. A lot of world things don't actually require game statistics unless you're going to be fighting them.