getopt modifies the @ARGV array. Before you call getopt, you can store the number of original args passed to the script, then use the new variable instead of $#ARGV:

use Getopt::Std;
use Data::Dumper;

my $arg_num = scalar @ARGV;

#Getting the command-line options
my %options = ();
getopt( "fdrv", \%options );

if ( exists $options{f} ) {
    if ( $arg_num != 7 ) {
        print "USAGE withouf option f\n";
    }
}

if ( not exists $options{f} ) {
    if ( $arg_num != 5 ) {
        print "USAGE without option f\n";
    }
}
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