In 3 quart pan, combine the water, salt, syrup, vinegar, and pepper corns. Bring to a boil over medium-high heat, stirring until the solids have completely dissolved into the liquid then combine with the ice water to cool immediately. Alternately, you can cool and refrigerate the mixture, before adding the additional water, until you are ready to brine your turkey.
When you are ready to brine the turkey, get out a large stock pot or line a large, clean, food safe bucket with a brining bag, secure the edges by folding them over the top of the bucket. Place the turkey and apples in the pot or bag then cover with the ice cold brine. Make sure the turkey is fully submerged in the brine, place a plate over the meat if needed to keep it in the liquid. Tie off your brine bag if using or cover your pot with the lid or plastic wrap.
Refrigerate the brining turkey for 40 minutes for every pound - 3 hours and 2 minutes for 5 lbs. When enough time has passed, remove the turkey from the brine, carefully discard the brine and all the additional ingredients. Pat the skin dry with paper towels and allow the meat to sit for 30 minutes to reach room temperature.
While the meat rests: Set the oven rack to the vertical center and pre-heat the oven to 425F. Slice a large onion and a large navel orange into ¼ inch rounds. Arrange the slices, rosemary, and thyme sprigs in an even layer in a roasting pan. Place the turkey, skin side up, on the onion and orange slices.
Roast the turkey for 45 minutes - 1 hour, until the thickest part of the thigh has reached 155F degrees. Remove the turkey from the oven, tent loosely with foil, and let rest 10-30 minutes - the temperature of the meat should continue to increase to 165F.