No no footballer yhas scored five goals in a single champion league game.
Lionel Messi, against Bayer Leverkusen on 7 March 2012
No individual has scored 6 goals in one game in Premier League era (4 players have scored 5)
Alan Shearer has scored the most (260) premier league goals.
It is four goals by Olle Gunner Solacer
The most goals scored in a single game is 11; 29-Sep-2007 : Portsmouth 7 - 4 Reading.
Top number of goals scored in a Premier League game: 11 goals. Portsmouth FC beat Reading FC 7-4 (29 September 2007)
Ole Gunnar Solskjaer, 4 goals.
If you are asking of the Barcelona verses Arsenal game , then David Villa scored the first goal.