Hi NaeBean,
The Brooklyn Bedding BestMattressEver is a latex/polyfoam hybrid that uses 2" of Talalay latex on top of 2" of synthetic continuous pour Dunlop latex on top of a 6" 2 lb polyfoam support core and it has a cover with a thin layer of polyfoam in the quilting so it doesn’t have latex from top to bottom and this would affect the type of support system that would be most suitable.
There is more about the different types of support systems that generally work best with different types of mattresses in post #1 here. There is also more about support systems that would be suitable for TheBestMattressEver (or other mattresses that use a similar support core) in this topic as well.
While 5" gaps between the slats would be the most I would consider … I would generally look for gaps that are about 4" or less and 3" would certainly be fine (even if the mattress had a latex support core) as long as there was a center beam with good center support to the floor.
Phoenix