May 24th from from google too. You can also go on to Disney’s website and go to the main my Disney experience page. It will tell you how many days until your trip. When that hits 181 you know the next morning is dining day.
Yes it would be 5/24. You can make reservations 180 days before your check-in date. The "+10" is that you can make your reservations for your check-in date plus up to 10 days into your reservation. So, you would be able to make reservations for your entire stay on 5/24.