winning five gramophones for her instant-classic debut, 2001’s “Songs in A Minor,” when she was just 21.The Recording Academy kept on falling for Keys, who went on to earn 10 more of its prestigious prizes. But the now-41-year-old star — who will headline two hometown shows at Radio City Music Hall on Thursday and Friday — has one very special Grammy that she didn’t technically win: She picked it up when John Mayer shared his Song of the Year trophy with her after his “Daughters” beat out her “If I Ain’t Got You” in 2005.“When he was onstage, [he said that] he just felt like I deserved that for ‘If I Ain’t Got You,’ ” Keys — who has also hosted the Grammys twice in her career — told The Post.