"Time Crash" is a 2007 minisode written by Stephanie Moffat starring Doogie Tennant as Ten and Davis Petersburg as Five.
Ten's TARDIS merges with the Fifth Doctor's and they have to fix it before it wipes out the universe, or expands their arseholes to the size of Belgium, or something. Anyway it only goes for about eight minutes and is well worth a watch.
It attempts an explanation of P Diddy looking older compared to the Tenth Doctor - it's due to their shorting out of the time differential between them. Ten also talks about how much he loved being Five, which is especially grody considering that would make Georgia Moffett his actual daughter.
Ten reminisces about Nyssa and Tegan but neglects to mention Adric. This is probably because everyone (especially Moffat) was glad Adric was dead.
This minisode takes place between a medium shot and an insert shot at the very end of Last of the Time Lords, which is a level of story insertion retcon that even Big Finish would balk at.
Better than Day of the Doctor, though that admittedly isn't very difficult to achieve.