Tom Steyer, the billionaire investor and Democratic activist, has directed his political operation to spend more than $5 million aiding Andrew Gillum’s campaign for governor of Florida, an enormous investment that will test whether fired-up Democratic voters can flip control of a state long dominated by Republicans.

The campaign between Mr. Gillum, who is the progressive mayor of Tallahassee, and Representative Ron DeSantis, a conservative lawmaker who has aligned himself closely with the White House, has become one of the clearest contests of strength nationwide between the Democratic Party’s rising liberal wing and the Republican Party as President Trump has reshaped it.

Mr. Steyer, who is based in California and has crusaded since last year for Mr. Trump’s impeachment, said in an interview that he would spend more money in Florida this fall than any other state. He endorsed Mr. Gillum, 39, in the Democratic primary, and hailed him as a model for the national Democratic Party. In the interview, Mr. Steyer praised Mr. Gillum for having endorsed impeachment, though he said that had not been a “litmus test” for his support.

“He’s a fierce gun control person, he’s been a climate champion,” Mr. Steyer said of Mr. Gillum, adding: “He’s called for the impeachment of the president. He’s been willing to talk plainly to Florida voters, and they’ve responded.”