Complex sentence: Thompson was approached by national Democrats about running for Congress in 1996 against freshman Republican Frank Riggs, but he declined, believing his senate seniority would be more beneficial to his district than would his being a freshman congressman.
Split into simpler sentences: Thompson was approached by national Democrats about running for Congress in 1996 against freshman Republican Frank Riggs. However, Thompson he declined, believing his senate seniority would be more beneficial to his district than would his being a freshman congressman.