Answer:
If the ratio of yes votes to no votes was 7 to 4, then there were a total of 7 + 4 = <<7+4=11>>11 yes and no votes.
Since there were 5896 total votes, the number of no votes was 4/11 * 5896 = <<4/11*5896=1928>>1928. Answer: boxed{1928}.
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