How do you know that the user is not going to rename whatever file they want to use to have an acceptable file extension? Why not use image::info? It can tell you the mime type or suggested extension for an image.

Untested code snippet:

use Image::Info qw(image_info);
my $filename = "file5.jpg"; # actually a PNG
my $info = image_info($filename);
if (my $error = $info->{error}) {
    die "Can't parse image info: $error\n";
}
my $mime_type = $info->{file_media_type};
my $suggested_ext = $info->{file_ext};
print "mime type: $mime_type\n";
print "suggested extension: $suggested_ext\n";
[download]

Output produced:
mime type: image/png
suggested extension: png

Then you can check against your list of good extensions.

Update: Code updated and tested!