There are several problems in your code:

my @array = join(' ' , keys %num) . "\n";
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You apply a string value (scalar) to an array. It looks like you are trying to print it. You probably want to do this:

my @array = keys %num;
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There is a simpler way to do realize your program:

my @num = ();
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It's easier to use an array, instead of hash for your program.

while(scalar @num < 5){
  push @num, int(rand(50) + 1);
}
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or, even easier:

push(@num, int(rand(50) + 1)) for(1..5);
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print join(' ' , @num), "\n";
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my $sum = 0;

for(@num){
  $sum += $_;
}

print "The sum is: $sum\n";
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Or, the final code:

my @num = ();

push(@num, int(rand(50) + 1)) for(1..5);

my $sum = 0;
for(@num){
  $sum += $_;
}

print join(' ' , @num), "\n";
print "The sum is: $sum\n";
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Or, group the loops:

my @num = ();
my $sum = 0;

for(1..5){
  my $num = int(rand(50) + 1);

  push(@num, $num);
  $sum += $num;
}

print join(' ' , @num), "\nThe sum is: $sum\n";
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