Show posts in category x and y from the 6th most recent post onwards

Without seeing your code, here’s a rundown that should work for you.

1. At the top of your template file, start an array, $featured_posts = array();
2. In your featured posts loop, in each iteration, add the ID of the post to the array, $featured_posts[] = get_the_ID();
3. In your second loop, check to see if the post was already displayed, and if so, skip to the next iteration of the loop: if ( in_array( get_the_ID(), $featured_posts ) ) continue;