Five Island, also known as Chrono Island, is where the Rocket Warehouse is located. However, before you start messing with Team Rocket, there are other better things to do. Surf west into the Water Labyrinth, and you'll find an old man on land. Talk to him, and he'll give you an Egg that once hatched will yield Togepi. Next, go east in the Water Labyrinth to reach the Resort Gorgeous section. You'll reach another island with some trainers and an empty house.
NOTE: Keep this area in mind if you find yourself short on money. Both the Lady trainers in the island with the house hand over around $10,000 Pokedollars per defeat. Use your VS Seeker on them, and in combination with the Amulet Coin you could make close to $40,000 with only two easy challenges!
Continue east and you'll reach the Lost Cave.
Lost Cave
This is a confusing cave filled with fog, and exits that never seem to go where you want to go. Follow these wise steps to navigate the cave: Go right, up, down, down, right, left, down, right, and up. After that, you'll reach Lady Selphy, who will battle you with two level 49 Persians. After defeating her, she'll take you to her house, which was the empty house you passed by earlier in Resort Gorgeous. Go talk to her when you have the Pokémon she wants to see, and she'll give you valuable items (usually a Luxury Ball). For items in the Lost Cave, go back and follow these steps for the items you want (beginning at the start):
- Lax Incense - right, down
- Max Revive - right, up, down, down, right, right
- Rare Candy - right, up, down, down, right, left, down, left
- Sea Incense - right, up, down, up
Rocket Warehouse
After taking care of all that, it's time to face Team Rocket. Either fly or walk back to the Pokémon Center, and go south from there. After a while, you'll reach Rocket Warehouse. Go inside, and you'll see that familiar spin maze. Play around with the maze, and as you do, be sure to pick up important items such as TM36 - Sludge Bomb and Up-Grade. You want to reach the Scientist in the upper-right hand corner. Fight him, and he'll give you back the Sapphire. Be sure to press 
against the box in this room for a Nest Ball. You're finally finished with the Rockets!
Now exit the Rocket Warehouse and surf west. Go up and pick up the PP Up. Now surf east a little to get to Memorial Pillar.
Memorial Pillar
Battle all the people on the strip of land, and surf south a bit more. You'll reach a larger island with a huge stone in the middle and a Metal Coat on the left. The huge rock is the grave of the trainer's Onix, Tectonix. If you leave a Lemonade there, the trainer will give you TM42 - Facade.
Now that everything's taken care of, go to One Island and hand Celio the Sapphire gem. With that, the machine is fixed, and now Pokémon from Ruby, Sapphire, and Emerald can be traded to FireRed and LeafGreen. In addition to that, you'll be able to fight the Elite Four again, and will also be able to catch Mewtwo in the Cerulean Cave in Cerulean City. If you fight the Elite Four again, they'll have stronger Pokémon, and you can do that on your own time. Now, it's time to catch the strongest Pokémon: Mewtwo!