MIAMI  Incumbent and establishment candidates beat back strong primary challenges, for the most part, on Tuesday in contests in five states across the country.

It was one of the last big nights of the 2010 primary season, before the all-important general election campaign that could decide who controls Congress and, inevitably, the warp and weft of the second half of President Obama’s term.

The results proved that in an election season where voter dissatisfaction is running high, established politicians cannot be counted out, even against insurgents who have considerable personal fortunes to bankroll their upstart campaigns.

In arguably the starkest example, the race to be Florida’s Democratic candidate for the United States Senate, Kendrick B. Meek, 43, a congressman from Miami, defeated Jeff Greene, a 55-year-old real estate mogul.