Overall, the poll finds Trump ahead in two of the states, Ms Harris ahead in one, and the pair tied in the remaining four.
Support for Ms Harris remains shaky in the “Blue Wall” of northern swing states after Mr Biden dropped out of the race in July.
She is also behind by two points in Arizona, which Mr Biden flipped blue for the first time since 1996, and in North Carolina, the only one of the swing states that Trump won in 2020.
Several reputable election models now predict that Trump will win next month’s election, returning him to the White House after four years in the political wilderness. He would be the second president in US history to serve two non-consecutive terms.
The individual decisions of the millions of switchers at this election will be closely scrutinised by both parties after election day, regardless of which candidate wins.
Telegraph analysis of a separate national poll, also by Redfield & Wilton Strategies, shows that Trump’s strength on the economy and immigration is driving the exodus of voters from Ms Harris’s campaign.