Double quotes interpolate variable values, and @- is a special variable. Use single quotes instead:

my $string = join ('-@-', sort@array);

# My output
# The string contains five-@-four-@-one-@-three-@-two
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UPDATE: Here is a quote from perlop which I think is a handy bit of trivia:

"Punctuation" arrays such as @* are usually interpolated only if the name is enclosed in braces @{*}, but the arrays @_ , @+ , and @- are interpolated even without braces.