What are the symptoms of the problem, i.e. works but messes up classes, doesn't work at all, etc.?
To start with, it looks like the condition
[Group] ="Group3 AND [Group]="Group5"
can never be true, as it means that the item belongs to both Group3 and Group5 at the same time. It probably should be
[Group] ="Group3 OR [Group]="Group5"
Also, Group4 rows will be automatically placed into NULL class, as you didn't specify how to handle them via ELSE.
Similar to what Dimitri said, but the calculation could be similar to the following:
IF [Group] = "Group1" THEN "Class A"
[Group] = "Group2 THEN "Class B"
[Group] ="Group3" then "Class C"
[Group]="Group5" then "Class C"
[Group]="Group4" then "No Class"