Remove giblets and neck from turkey, and discard. Rinse turkey with cold water; pat dry. Set aside.
Stir together 1/2 cup apple juice and brown sugar in a large saucepan over low heat until sugar dissolves. Remove from heat, and add cider vinegar and remaining 4 1/2 cups apple juice.
Place turkey in a large roasting pan. Cover turkey with cheesecloth. Pour juice mixture over cheesecloth, coating completely. Cover and chill at least 8 hours, spooning marinade over turkey occasionally.
Remove turkey from pan, discarding cheesecloth and reserving 3 1/4 cups marinade.
Place turkey on a rack in a large roasting pan. Pour 2 1/2 cups reserved apple cider marinade over turkey.
Bake at 325° for 3 hours and 15 minutes or until a meat thermometer inserted into thigh registers 172°, basting every 30 minutes with pan juices. Shield with aluminum foil to prevent excessive browning, if necessary. Let stand 15 minutes or until meat thermometer registers 180°.
Remove turkey to a serving platter, reserving 2 cups pan drippings. Pour reserved drippings through a wire-mesh strainer into a saucepan, discarding solids. Add 1/4 cup reserved marinade, chicken broth, brandy, and honey to saucepan, whisking until mixture is smooth.
Stir together flour and remaining 1/2 cup reserved marinade; add broth mixture. Bring to a boil, stirring constantly. Reduce heat to low, and cook, stirring occasionally, 15 minutes or until thickened. Add salt and pepper to taste. Serve with turkey.