In Pokemon Red, the fifth badge is possessed by the Poison-Type Koga. The badge is named Soul Badge. It lets you use Surf outside of Battle.
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you should use either ground or psychic Pokemon
You need to defeat Koga in Fuchsia City to get the 5th badge, the Soul Badge.
The fifth badge is in Sootopolis City, you need Surf, Dive, and Whirlpool to get it
The 8 badges for Pokemon Red are: Boulder Badge, (Brock) Cascade Badge, (Misty) Thunder Badge, (Lt. Surge) Rainbow Badge, (Erika) Marsh Badge, (Sabrina) Soul Badge, (Koga) Volcano Badge, (Blaine) and Earth Badge. (Giovanni)
In Pokekon Sapphire, you get the 5th badge after defeating your opponent in a Gym Battle at Petalburgh.