Escape the backslash: 
    $line =~ s/A.TL5F00/+TL\\F5C/g;

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Tip #1 from the Basic debugging checklist: diagnostics might give you a little more info (it didn't for me on Perl version 5.12, but it did for 5.14).

Did you really want the print inside the while loop? while ( $line = <FILE> ) { is really the same as while (defined($line = <FILE>)) {. So, outside the while, $line is undefined.

UPDATE: You can simplify the if/else code with this single substitution: 

use warnings;
use strict;

while (my $line = <DATA>) {
    $line =~ s/^A.TL5([EF])00/+TL\\${1}5C/g;
    print $line;
}

__DATA__
A.TL5E001100.TAV
A.TL5F001100.TAV

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In reply to Re: Substitute script for a newbie by toolic
in thread Substitute script for a newbie by jspanos

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