Short answer:        @sorted = sort @unsorted Discussion:
There are some marvelously creative solutions proposed here. But I must be missing something.

IF
The 'A' characters always appear in the two places illustrated...
and the data is always zero-padded as shown...
and you want to sort first by the second column...
and then by the third column...
                            Update: shaezi has confirmed these assumptions.

Won't a standard sort do the job simply and efficiently?

my @unsorted = (
    'A 00006360 A001054054 000000000.00',
    'A 00006360 A001002002 000000000.00', 
    'A 00006360 A001012012 000000000.00',
    'A 00005460 A001102002 000000000.00',
    'A 00007360 A003015015 000000000.00');

my @sorted = sort @unsorted;

print "$_\n" for @sorted;
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dragonchild mentioned the single-dimensioned array possibility but then moved away from it. And no one else seems to have considered doing it this way. So it is with some trepidation that I offer this solution. But...