A new CBS News poll of Florida's Senate race shows Gov. Rick Scott with a 5-point advantage over Sen. Bill Nelson, 46-41 percent, in a survey with a margin of error of 3.5 percent — another sign of a close contest.

Nearly five months before the election, the survey shows only 6 percent of voters are not sure of their preference in a battle in which both candidates and like-minded groups will spend tens of millions of dollars on TV ads to sway relatively few voters' minds.

The poll shows 62 percent of voters approve of Scott's handling of his job and 54 percent approve of Nelson's.

A solid majority (59 percent) favors stricter gun control laws.

On how things are going in Florida, always a key test for a sitting governor, 53 percent said things are going very well or somewhat well and 47 percent said somewhat badly or very badly. In a positive sign for Scott, 70 percent said "the availability of good jobs" in Florida is going well.

The poll suggests the two candidates are running dead even with Hispanic voters (Nelson 37 percent, Scott 36 percent, 22 percent not sure).

Asked about President Donald Trump, 52 percent approve of his job performance and 48 percent disapprove. In addition, 36 percent of poll respondents say they want a senator who tries to support Donald Trump as much as they can compared to 24 percent who said they want a senator who tries to oppose Trump as much as possible.

On key issues, 59 percent said immigration is going somewhat badly or very badly in Florida. The next closest issue was health care, with 47 percent saying badly or very badly.

That's a potential plus for Nelson, a critic of Scott for reversing course on Medicaid expansion.

The poll of 1,002 Florida voters was conducted June 19-22 by YouGov.