Walkthrough
After obtaining the S.S. Ticket from Bill on Route 25 and defeating Team Rocket in Cerulean City afterwards, you can proceed south on Route 5. This is a small route that contains on a few Wild Pokemon and the Pokemon Daycare. Route 5 leads to Saffron City, but, unfortunately, you won't have access to it at this time. Instead, you will need to take the Underground Path 5-6 to reach Route 6.
Wild Pokemon
Grasses:
Pidgey (40%): Levels 13-16
Meowth (35%): Levels 10-16
Oddish(FireRed)/Bellsprout(LeafGreen) (25%): Levels 13-16
Surfing:
Psyduck(FireRed)/Slowpoke(LeafGreen) (100%): Levels 20-40
Magikarp (100%): Level 5
Poliwag (60%): Levels 5-15
Goldeen (20%): Levels 5-15
Magikarp (20%): Levels 5-15
Poliwag (40%): Levels 15-25
Poliwhirl (40%): Levels 20-30
Gyarados (15%): Levels 15-25
Psyduck(FireRed)/Slowpoke(LeafGreen) (5%): Levels 15-35
Pokemon Trainers
Bug Catcher Keigo: Level 16 Weedle, Level 16 Caterpie, Level 16 Weedle
Camper Rickey: Level 20 Squirtle
Picnicker Nancy: Level 16 Rattata, Level 16 Pikachu
Bug Catcher Elijah: Level 20 Butterfree
Picnicker Isabelle: Level 16 Pidgey, Level 16 Pidgey Level 16 Pidgey
Camper Jeff: Level 16 Spearow, Level 16 Raticate
Pokemon Trainers - VS Seeker Rematch
Camper Rickey: Level 22 Squirtle
Camper Rickey: Level 30 Wartortle
Camper Rickey: Level 55 Wartortle
Picnicker Isabelle: Level 21 Pidgeotto, Level 21 Pidgeotto, Level 18 Pidgey
Picnicker Isabelle: Level 29 Pidgeotto, Level 29 Pidgeotto, Level 26 Pidgeotto
Picnicker Isabelle: Level 47 Pidgeotto, Level 47 Pidgeotto, Level 50 Pidgeot
Camper Jeff: Level 21 Spearow, Level 21 Raticate
Camper Jeff: Level 29 Fearow, Level 29 Raticate
Camper Jeff: Level 54 Fearow, Level 54 Raticate
Items
Rare Candy: ItemFinder
Sitrus Berry: ItemFinder