Only five teams? That won't work in the NFL 'cause the NFL is about money. With the current format you have eight different teams in the playoffs.
5 in each conference sorry, we call it the final 5 because we only have one league. lol I'll explain it to you in case you're unfamiliar, in actual fact you get more games out of it than the current set up. I'll use the NFC as an example.
Week 1 - Qualifying Playoffs
Game NFC-A: Team 4 v Team 5 @ Team 4 (loser eliminated)
Game NFC-B: Team 2 v Team 3 @ Team 2 (winner plays Team 1)
Team 1 BYE
Week 2 - Qualifying Semi-Finals
Game NFC-C: Loser Game B v Winner Game A @ Loser B (loser eliminated)
Game NFC-D: Team 1 v Winner Game B @ Team 1 (winner to Week 3 Conference Championship)
Week 3 - Qualifying Final
Game NFC-E: Loser D v Winner C @ Loser D (loser eliminated)
Week 4 - Conference Championship
Game NFC-F: Winner D v Winner E @ Winner D (Winner to Super Bowl)
Week 5 - Superbowl
Game G: Winner NFC v Winner AFC
Essentially the format gives Team 1 a second chance in case they lose their first game whilst also giving them home field advantage, Team 5 on the other hand has to play every match sudden death and away from home.