How to upgrade MySQL to a New version..?
There's a PPA that someone has created which includes MySQL 5.5.  Since PPA's are community-contributed, the usual warnings about using with caution apply.

There is a guide in the MySQL docs for some standard practices to follow when upgrading from one version level to another.

Edit:

Here is some information from the mysql_upgrade manual page that should give you an idea of why it's important. This is in response to your comment.


  mysql_upgrade examines all tables in all databases for
  incompatibilities with the current version of MySQL Server.
  mysql_upgrade also upgrades the system tables so that you can take
  advantage of new privileges or capabilities that might have been
  added.
  
  mysql_upgrade should be executed each time you upgrade MySQL. It
  supersedes the older mysql_fix_privilege_tables script, which has been
  removed in MySQL 5.5.
  
  If mysql_upgrade finds that a table has a possible incompatibility, it
  performs a table check and, if problems are found, attempts a table
  repair.