The short answer is that they didn't, exactly. The game is scaled for 4-6 player characters, with five being the convenient midpoint for the DM to easily scale up or down published adventure modules.
From the 4e DMG (p31):
This book provides rules and guidelines for running
a group of four to six player characters. If your group
varies from that size, you have some specific issues to
The sections "Smaller Than Four" and "Larger Than Six" address in what ways the game breaks down at these scales.
The slightly longer answer is that early encounter design grew out of experiences the designers had playing "more fun" engagements in miniatures combat. From "Wizards Presents: Worlds and Monsters," designer James Wyatt says,
When we started designing 4th Edition, we quickly discovered
that we all shared the same experience. Encounters with
multiple monsters are just more fun. So we began with a new
assumption: The baseline encounter for a group of five PCs of
level X is four monsters of level X.
Although that still puts the ratio in terms of players::monsters, Wyatt goes on to clarify he views encounter design from the POV of the monsters, (or more generally, the DM running the monsters) rather than the players. One such excerpt (same book):
if you design an encounter aiming for four monsters,
it’s a lot easier to use all the roles. A mind flayer might have a
bodyguard of advanced grimlocks—controller plus melee. A
thug in an alley is supported by backstabbers lurking in the
shadows—melee plus lurkers. A pair of ogres shield an orc
archer and a shaman—melee, artillery, mastermind. Highly
mobile drow control a giant spider that emerges from the shad-
ows to pick off isolated PCs—skirmishers with a lurker. The
possibilities are endless, varied, and extremely fascinating.
So from that perspective, your question ("Why did the D&D 4e designers scale everything for 5 players?") doesn't reflect the designers' initial thought process. Instead, it would be, "How many players (within the sweet spot of 4-6) are needed to deal with a fun encounter of four monsters of varied roles?"