Stamp: Laughing Sprixie
This path opens up once you've cleared World 5-5. Enter the tent to claim your prize.
World 5-B: Fire Bros. Hideout #2
You can reach this by examining the ground left of World 5-5. Take the warp pipe that spawns to get there. Once there, take out the Fire Bro. riding the Goomba stack to earn a star.
World 5-6: Cakewalk Flip
When you reach the first big section of flip panels, time your jumps so that you have a blue panel in the upper left corner. There's a star here.
Take out the Piranha Plant just past the checkpoint and use his warp pipe. In this hidden area, you have to guide the green ball to the tile on the bottom left. Use your jumps in conjunction with the flip panels to make it work, and you'll earn a star for your efforts.
After the secret area, you'll come to two rows of flips panels. Hit the hollow green star in the top left to spawn eight green coins. Use your jumps carefully to collect them along the flip panels, and you'll receive a star.
If you manage to bring at least two Double Cherry clones through the whole level, you can hop on the two-man platform at the end to reach a stamp.
World 5-7: Searchlight Sneak
The first star is pretty tricky to grab. When you reach the fourth faux trampoline, stun him and pick him up. Rush through the spotlight and avoid the Cat Suit Bullet Bills. Now you can safely use the trampoline to reach the star above.
The stamp is also tricky to grab. Immediately after the checkpoint, you'll see it above a row of bricks. Carefully jump up there and grab it before the searchlight spots you.
Just past the stamp is a cracked wall. Step into a searchlight to be swarmed by Cat Suit Bullet Bills. Lead one into the cracked wall to blow it away, revealing a mystery box. Inside, there will be a star atop some blocks and a constant barrage of Cat Suit Bullet Bills. Quickly and carefully grab the star to get out of there.
You'll find the last star while scaling the vertical wall at the level's end. Let yourself be seen by the searchlight, and lead the Cat Suit Bullet Bills into the big bricks to break through to your prize.
World 5-Special: Captain Toad Plays Peek-a-Boo
Start by heading through the first purple door. Use the touch platform to reach the first star on the ledge above.
Head down the slope and through the left door to reach the ledge above. Grab the star and enter the door on the right.
Drop from the ledge and follow the red platform. Touch the upper platform to move it forward, then drop into the dip it blocked. Step onto the first touch platform, then tap to raise yourself to the second. Hop to it, then tap to raise yourself to the walkway by the sliding platform. Step onto it and give it a touch to slide out into range of another star.
Ride the platform back, then step through the archway and round the corner. Time your walk between the ghosts to grab the star here.
Head up the hill and follow the path. When you hit the long stretch of falling platforms, a Big Boo appears. Stare at it to keep it from attacking you, then ride the falling platform down to the last star.
World 5-Castle: King Ka-Thunk's Castle
Early in the level, you'll come across a hollow green star. Hit it to spawn eight green coins. If you collect them all before they disappear, you'll earn a star.
Stamp: Chargin' Chuck
When you reach the cart-wheeling spike squares, use a Cat Suit to scramble up the wall. There's a stamp on the ledge here.
The second star is found inside the last of the cart-wheeling spike squares. It will appear in the center of every other square, so just wait a moment if you miss it.
Before heading through the warp box at the end of this section, use a Cat Suit to scramble up the nearby wall. There's one last star up here.