On 2003’s Coverage, Mandy Moore showed she had good taste — covering XTC, Joni Mitchell, Joe Jackson, etc. — but artistically, she was still stuck in a candy-pop bubble. Now, on her fifth album, she finally tries to tell her own story, with co-writing help from singer/songwriters Rachael Yamagata and Lori McKenna, as well as Boston folk-pop duo the Weepies. The tunes are catchy and heartfelt, as Moore moves from lush ballads to acoustic folk that recalls Patty Griffin. “It’s been good, getting to know me more,” she confesses in “Gardenia,” and with songs so warmly soul-searching, it’s easy to second that emotion.