Umm, in this case, you really don't have to do anything special. This worked fine for me:

my @array = <DATA>;
@array = sort { $a cmp $b } @array;
print @array;
__DATA__
100!100!key!date!2..
100!100!key!store!
110!110!P\d\d\d_.*\.\d{6,}\.EMRemr
120!125!
1!yeada
130!132!
140!133!
150!134!
500!blah
160!135!arbor_ama
503!blah
170!136!
505!blah
180!137!
190!138!
[download]

It produces:

1!yeada
100!100!key!date!2..
100!100!key!store!
110!110!P\d\d\d_.*\.\d{6,}\.EMRemr
120!125!
130!132!
140!133!
150!134!
160!135!arbor_ama
170!136!
180!137!
190!138!
500!blah
503!blah
505!blah
[download]

I don't know if it's just the sample data you're using, but from your output, you really want to sort on the whole line, lexicographically.

HTH