4th
the badge you need is the 4th one and also if you have not already you can get surf in the dance theater.
3
You need the correct gym badge(s) for your Pokemon to use Surf out of battle.
Teach surf to a Pokemon and click the water and it will ask u to surf. You will need a certain gym badge,though.
The fifth badge is in Sootopolis City, you need Surf, Dive, and Whirlpool to get it
You need the soul badge that is obtained from defeating the Fuschia city gym leader Koga in order to use surf outside of battle.
It is in Cherrygrove City. You will need a pokémon that knows Surf and the appropriate badge. To the south west of the city is some water, surf there and talk to the guy standing on the island, he will give it to you.
you have to defeat the fuchsia gym leader.
the one you get from the gym in fuschia city.
You need 4 badges.
On cinnabar island. You can get to Cinnabar by using surf from Pallet Town. To use surf, you need to get Fuschias gym badge.
it's the badge from crasher wake