The solution is to store the last 5 lines visited in an array, and also have a variable tracking how many more lines beyond the current one have to be output:

$x = 5; # Number of lines to print above and below.

open (LOG, "GWSvc.log") || die "Unable to get a handle to the file: $!
+\n";

$after = 0;
while (<LOG>) {
    if ($after) {
        print $_; $after--;
    }
    else {
        push (@lines, $_);
        if ($#lines > $x) { shift(@lines); }
    }
    if (/c9391b56-b174-441b-921c-7d63/) {
        print $line while ($line = shift(@lines));
        $after = $x;
    }
}
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