Use a dispatch handler.

my %handlers = (
   first  => \&display_first,
   second => \&display_second,
   ...
);

my $handler = $handlers{$query->param( "button" )};

if (!$handler) {
   ...
}

$handler->($query, $region, $var1, $var2, $var3);
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You might even want to make some of those variables global, especially if they aren't changed after being set. Alternatively, the handler could use $query to get the variables it needs.