Beat the fuchsia city gym leader.
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.
you should use either ground or psychic Pokemon
the fifth badge is from Sabrina in Saffron City.
Fuschia city.
hearthome city
Hearthome
Hearthome City.
Petalburg City.
Beat the gym leader
The fifth gym leader in Pokemon platinum is crasher wake but you get the fourth badge.
You need to defeat Koga in Fuchsia City to get the 5th badge, the Soul Badge.
The Cascade Badge