What is my religious obligation after having vandalized someone's website five years ago when I was thirteen years old, knowing that the perpetrator was not identified?

Material rights must be returned to their owners or their forgiveness sought. If the website is free of anything forbidden, then one of two things is incumbent upon you: either seek forgiveness from the person concerned, even if indirectly (such as sending an anonymous repentance message, or mediating through someone who seeks forgiveness on your behalf without mentioning your name), or restore the website to him ready and deliver it indirectly.