The first thing I’d say about this program is ... “always use real variables,” not “implied” stuff like $_ which can very easily get away from you.   Then, “start with a test case.” One example string, that you can verify gets correctly parsed by the regular-expression you intend to use.   You can even use a “Perl one-liner” like this:

perl -e 'my $str = "chr1:4777082-4777141"; \
  my ($foo) = $str =~ /([0-9]+)/; print "foo is $foo\n";'
foo is 1

... oops, that's not right ...

mike$ perl -e 'my $str = "chr1:4777082-4777141"; \
  my ($foo) = $str =~ /[:]([0-9]+)/; print "foo is $foo\n";'
foo is 4777082

... correct.
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Now, write your program, something like:

while (my $str = <INFILE>) {
  my ($foo) = $str =~ /[:]([0-9]+)/;  # WE TESTED THIS
  die "Something's Wrong with $str!"
    unless ($foo);   # NEVER ASSUME, NEVER ASSUME
  print OUTFILE "FILE=$foo\n";  # NOTICE DOUBLE-QUOTES
}
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We used the one-liners to verify the actual regular-expression parsing, to quickly get it right (and to uncover a subtle bug in the first attempt), then wrote code that is above all else, clear to do the actual work.

Within that program, we also added a die statement that will cause the program to test its assumption that every single record of the input will be handled correctly.   (We could make this test even-more aggressive if we knew that every record of the input file should contain seven digits, preceded by a ":" and followed by a "-", with: (see bold-faced parts)
/[:]([0-9]{7})[-]/)
Thus, the very fact that the program runs normally to completion, with a very stringent regular-expression that must be matched every time, is a strong indication that both the input data and the resulting output are correct.