In Pokémon Black, if the player doesn't capture Reshiram at N's Castle, due to having a full party and full PC Box,
Reshiram can be encountered at the highest level of the Dragonspiral Tower after becoming Champion.
In Pokémon White 2, after the player defeats N in the ruins of N's Castle, the player will be given a Light Stone.
When the Light Stone is brought to the peak of the Dragonspiral Tower, Reshiram will awaken, and can be challenged to a battle.
Reshiram cannot be encountered shiny in Generation 5.