I would like only products that have qty=>5 to be marked as in stock, those that are less than five would be marked as out of stock and they won't be available for sale.
You can make products with positive qty out of stock from admin setting
Admin >> Store >> Configuration >> Catalog >> Inventory >> Product Stock Option >> Out-of-Stock Threshold
Add 5 to here and check any product with qty value 5. It will auto out of stock.
I believe you can do this on Magento 1 by going to
System-Configuration-Catalog-Inventory-Product Stock Options
And adjusting the value for ' Qty for items status to become out of stock'