Prepare the jars. Wash the jars with hot, soapy water, then place them in a water bath canner filled with water and heat over medium heat until simmering. Keep the jars hot until ready to fill.
Wash the lids and rings. Clean the rings and new lids with hot, soapy water and set aside.
Set up your water stations. Bring a large pot of water to a boil and fill a large bowl with ice water. Set both within reach.
Make the syrup. In another large pot, combine the sugar and 5 cups of water. Stir over medium heat and bring to a slow boil, then reduce to a simmer, cover, and keep warm.
Score the peaches. Using a sharp knife, cut a small X on the bottom of each peach to make peeling easier.
Blanch the peaches. Working in batches of 3 to 4, place the peaches in the boiling water for 1 to 3 minutes, until the skins begin to loosen.
Shock in ice water. Immediately transfer the blanched peaches to the ice water bath to stop the cooking.
Peel and slice. Once cool enough to handle, peel away the skins and discard them. Cut the peaches in half, remove the pits, and slice into your desired size.
Simmer in syrup. Add the peach slices to the hot syrup and simmer for 5 minutes.
Pack the jars. Using a slotted spoon, fill the hot jars with peach slices, leaving ½ inch headspace.
Add the syrup. Ladle the warm syrup over the peaches, maintaining the ½ inch headspace.
Remove air bubbles. Run a bubble remover or chopstick around the inside of each jar to release trapped air. Add more syrup if needed to keep the headspace at ½ inch.
Seal the jars. Wipe the jar rims clean and apply the lids and rings until fingertip tight.
Load the canner. Transfer the jars to the prepared water bath canner, making sure there is at least one inch of water above the jars.
Process the jars. Cover the canner and bring the water to a full rolling boil. Once boiling, process pint jars for 20 minutes and quart jars for 25 minutes.
Rest in the canner. Remove the canner from the heat, take off the lid, and let the jars settle in the water for 5 minutes.
Cool the jars. Carefully lift the jars onto a cooling rack or a towel-covered countertop. Let them cool undisturbed for 12 to 24 hours.
Check the seals. Once cool, remove the rings and check that each lid has sealed properly. Store sealed jars in a cool, dark place. Refrigerate any unsealed jars and use within 1 week.