Since Mounting a Coordinator Assault!, Ash and Dawn are often seen exchanging high fives whenever one of them accomplishes something, which might possibly portray a friendship.
Dawn's Buneary has a crush on Ash's Pikachu. This could be a sign that Dawn may have a crush on Ash, since Professor Oak and Brock have said in the past that Pokémon represent the feelings of their masters and when two Pokémon fall in love, there is a good chance the Trainers will too. It is to be pointed out that Buneary developed this crush before Dawn caught it. The claim has also been refuted at various points during the series, so the feelings of the Pokémon are not always definitive to the feelings of the Trainers.
Ash has watched all of Dawn's Contests. He did not do this with May because he would sometimes be training his Pokémon instead of watching her.
Dawn is the source of some of the moves and strategies used in battle by Ash, which include Ice Aqua Jet & Spin. Ash watching Dawn's Contest may (in part) be so he can learn new things to apply in battle, though some say this is because of advice given to him by others.
One of the movie posters for Giratina and the Sky Warrior depicts Pikachu and Piplup sitting on Ash's and Dawn's heads, respectively. Some fans have pointed out that the distance portrayed between Dawn and Ash is very small. However, other fans point out how Ash's hair, which can usually be seen from the sides of his hat, is not present. This may mean the Trainers are not really wearing their hats.
Pearlshipping in the Japanese opening High Touch!High Touch!
The opening is sung by Ash and Dawn. The lyrics show how close their friendship is to each other and their Pokémon. But, mainly to each other.
Wild in the Streets!
While Dawn battled a revived Aerodactyl, Ash is fascinated with Piplup and Buneary's new dodging tactic that he asks Dawn to help him practice for his rematch. He then has Pikachu, Aipom, and Turtwig use them in O'er the Rampardos We Watched in his rematch with Roark, again in Getting the Pre-Contest Titters in his match against Kenny, and a few other times since, the tactic becoming a regular (if not frequent) feature in Ash's strategy.
Hold the Phione!
When Ash and Dawn were in the submarine, they saw a school of Luvdisc. Some PearlShippers consider this a hint because Luvdisc's Pokédex entry says if two people see a school of Luvdisc, they will be blessed with eternal love (however, there's been long-debated discrepancies about how much the anime and the game are relatable, and should not be taken at face value. Also, AdvanceShippers have a similar hint from the ninth movie).
