Complex sentence: He has been nominated for several MMVAs (Much Music Video Awards) his video for "Try Honesty" won the 2004 Best Rock Video award at the MMVAs and "River Below" won the Best Video, and Best Rock Video awards at the 2005 MMVAs.
Split into simpler sentences: He has been nominated for several MMVAs (Much Music Video Awards). His video for "Try Honesty" won the 2004 Best Rock Video award at the MMVAs and "River Below" won the Best Video, and Best Rock Video awards at the 2005 MMVAs.