You have to remember that there are different spots in the time line here. The events of Time Crash have already happened to the 5th doctor so he recognizes his future self, while Time crash is at least one year in the 10th doctors timeline.
What you’ve never heard of Time Crash? That is because it was a special broadcast for the annual Children in Need event in England. It was only broadcast once.
To my knowledge it is not available on DVD and I’ve never seen it broadcast on the US. If you watch it I suggest sending the charity a five spot since that it what it was for.