Bit of a general trivia question here and not necessarily related to the show, but does anyone know why the series of Great Rings goes 1, 3, 7, 9? By this I mean, why is there no set of five rings of power?

From the Silmarillion, it is said that the Elves made many rings of power under the watchful eye of Sauron, and he himself made the One Ring in secret to rule the others. After he did this the elves hid away three of the rings of power for themselves, while Sauron eventually came to possess many others. From these he gave seven to the Dwarf Lords and nine to the Lords of Men.

So in my understanding the rings of power had varying abilities and all but the One Ring were Elven, presumably to be used by the Elves alone until their corruption. But this means that Tolkien could have had Sauron give any number of rings to those whom he wanted to bring to his side. Sauron could have given five rings to the Dwarf Lords and seven to men, or if it is important for there to be seven Dwarven Kingdoms, he could have given five to men and seven to the Dwarves.

Why this avoidance of the number five?