Technically, two actors played the role of the first Doctor in 
"The Five Doctors."

The original first Doctor, William Hartnell, appeared in a 
sequence preceding the opening titles.  The sequence was a 
clip taken from "Flashpoint," the sixth episode of the serial 
"The Dalek Invasion of Earth."

For the narrative of the story, the first Doctor was played by 
Richard Hurndall.

"Consideration was apparently given around July, 1982 to 
casting Geoffrey Bayldon, who had appeared in the season 
seventeen story 'The Creature from the Pit,' but the part was 
eventually offered to Richard Hurndall, whom Nathan-Turner 
has seen in an episode of _Blake's 7_ and considered to 
resemble Hartnell.  Hurndall accepted the offer on 
6 October 1982."

Howe, David J; Mark Stammers, and Stephens James Walker. 
_Doctor Who: The Eighties_ (London : Doctor Who, 1996): 48.