inspired by your use of sum, the expected sum(1..n) = n*(n+1)/2, so take the found sum from the expected sum:

use List::Util qw(sum);
my @arr=(1..3,5..7); 
print +(1+@arr)*(2+@arr)/2 - sum(@arr);
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update: clarification = use 1+ and 2+ here because an element is missing from @arr