Route 5
After beating the Nimbasa Gym, it's time to head west out of town onto Route 5. You won't make it very far before Cheren shows up and challenges you to another battle. He now has a Lv. 24 Liepard, a Lv. 24 Pansage/Pansear/Panpour, a Lv. 24 Tranquill, and a Lv. 26 Dewott/Servine/Pignite. After defeating Cheren, Elesa will show up and introduce you to the Pokémon League Champion: Alder. He sets up a double battle for you and Cheren with two pre-schoolers. He'll then send you on your way.
If you speak to the man playing guitar here and then defeat him in battle you'll get the Electric Guitar. There are a couple of other trainers in this crowd you can battle, as well as several trainers and items in the grassy area to the north. If you head up there you can pick up a Great Ball, a Revive, and a Zinc. You can also find a Hyper Potion by taking the narrow path below the fence. Then continue ahead to meet up with Cheren and Elesa again. Elesa will let the drawbridge down, allowing you to continue.
Driftveil City
Somehow there are a few people on this drawbridge, despite it just being let down. There's nothing to do here though so just continue on ahead to Drifveil City. Cross this smaller bridge up ahead to find Cheren speaking with Clay, who is the next gym leader. Apparently letting the drawbridge down gave Team Plasma an escape route out of the city, so he says it's our job to go find them now.
Heal up at the Pokémon Center here if you need to, then there is a few optional pickups you can nab while you're here. If you speak to the man on the motorcycle he'll introduce you to Rotation Battles, a battle system where you can rotate through your Pokémon before attacking each turn. Enter the market here from the left and you can steal a Big Pearl from behind the counter.
In the northeast house in the block of four houses, speak to the man inside to get a Shell Bell if you've seen more than 50 Pokémon. In the house north of the market, you can get a Heart Scale if you show the woman inside a Pokémon that knows the move Echoed Voice.
Cold Storage
If you head south out of town, there is a Cold Storage area. There are a few trainers here that you can battle if you'd like. If you head south you can pick up a Ether in the grass to the right. Continue to the right to find another trainer as well as a Protein. Head back left in this south area and you'll run into Cheren who suggests that Team Plasma might be in the Cold Storage warehouse. Before heading in, go behind the building to find another Heart Scale.
Inside the building you can take the first set of stairs to find a Net Ball. You can then slide around on the first large patch of ice (enter from the far left) and find TM55 - Scald. There's a trainer here to battle, then you can head right across the ice and keep climbing the storage containers.
There will be a few trainers to battle along the way as you make your way on top of the containers and back down to the floor to the south. You can pick up the Ice Heal here before continuing north across the ice. Battle another trainer here and pick up the Hyper Potion to the right of him. Cheren will show up as you get to the end and you can enter the open shipping container together.
Inside you'll find a group of Team Plasma grunts huddled up for warmth around one of their sages. You'll be tasked with defeating the right half of the grunts starting with the one in front of you. The first has a Lv. 23 Watchog and a Lv. 23 Scraggy. The second has a Lv. 24 Liepard. The third has a Lv. 24 Trubbish. And the fourth has a Lv. 23 Sandile and a Lv. 23 Watchog. After defeating them all Clay will come in with some workers and escort them all out. Make sure to pick up the NeverMeltIce on your way out.
Driftveil Gym
When you approach Drivtveil Gym you'll see Ghetis and Clay in a standoff to return the captured Team Plasma members. Clay eventually hands them over since he is outnumbered. You are then free to take on this gym; it features Ground-type Pokémon. Grass-types will do especially well here, since there are few dual Water/Ground type Pokémon you'll be up against. Speak to the guide when you get in to get a Fresh Water. The puzzle in this gym is a series of elevator platforms that you can move up and down with switches.
Head to the first platform and move it down, then take on Worker Felix and his Lv. 28 Palpitoad and Lv. 28 Drilbur to the right. Head down on this platform and then move to the next platform in front of you. You can take it up for an optional battle with Worker Sterling who has a Lv. 28 Sandile and a Lv. Drilbur if you'd like, but otherwise walk left along the narrow ground behind it. You'll then need to defeat Worker Don and his Lv. 29 Krokorok before hopping on the next platform.
Take this platform down, and then you can head left and up for a battle with Clerk Isaac who has two Lv. 27 Sandile and a Lv. 27 Palpitoad, or you can skip it by just taking the platform in front of you up. Take the narrow platform to the right and you'll need to defeat Clerk Katie and her Lv. 29 Drilbur. You can then take this next platform all the way down to the gym leader, but if you need to heal up first you have a quick route back to the entrance by taking the south platform.
Gym Leader Clay
It's now time for your battle against the Ground-type specialist Gym Leader Clay. He uses a Lv. 29 Krokorok, a Lv. 29 Palpitoad, and a Lv. 31 Excadrill. The Excadrill can be quite tricky to deal with, as it's Steel-typing negates most of the Ground-type weaknesses. But Water-type moves should still do the trick. Don't keep Excadrill around too long though, as it will use Hone Claws to keep boosting its already high Attack stat. Clay also has two Hyper Potions he will use at the first opportunity.
After winning you'll get the Quake Badge, meaning Pokémon up to Lv. 60 will obey you. He says that he'll also give you a TM, but wants you to meet him at the end of Route 6 to collect it instead. We'll do that in the next chapter.
Back to Nimbasa Gym Continue to Mistralton Gym
