Instructions
Enter the Silph Co. building located at the center of Saffron City. Take the elevator in the main level up to the 11th floor. Watch the scene to find that you cannot enter the board room.
Head south to the Team Rocket Grunt and battle him. Three of his Pokemon are Rattata. Use Fighting-Type Pokemon to ease the difficulty of the battle. Take the Zinc he was guarding and use the elevator to reach the fifth floor.
Pass by the green warp tile without stepping onto it and proceed south. Battle the Team Rocket Grunt by using a Bug, Ghost, or Dark-type Pokemon against his Hypno.
Battle Juggler Dalton's Kadabra and Mr. Mime with Bug, Ghost, or Dark-type Pokemon and proceed on to battle Scientist Beau with Fighting, Ground, or Fire-type Pokemon.
Move south from the scientist to engage in a battle with another Team Rocket Grunt who uses an Arbok. Use Ground or Psychic-type Pokemon against the Arbok.
Walk onto the warp panel directly past the Team Rocket Grunt. Walk off and back onto the panel you emerge from to return to the fifth floor.
Proceed south off the panel to reach the Card Key. Press "A" to grab the Card Key which can be used to access all doors in the Silph Co. building.