Story highlights A poll shows Clinton leading Trump by five points in Arizona

Clinton would become the first Democrat to carry the state since her husband, Bill Clinton, won there in 1996

(CNN) A new poll shows Democrat Hillary Clinton with a lead in the traditional Republican stronghold of Arizona, yet another sign of Donald Trump's shrinking path to the nomination.

The survey, released jointly by the Arizona Republic, Arizona State University's Morrison Institute for Public Policy and Cronkite News , showed Clinton with the support of 43% of the state's likely voters, compared with 38% who said they intend to back Trump. Libertarian Party nominee Gary Johnson and Green Party nominee Jill Stein picked up the support of 7% and 4%, respectively.

There are increasing signs that Clinton could be poised for an upset in Arizona, which has a large Hispanic population unreceptive to Trump's hardline immigration rhetoric. A Democrat hasn't carried the state since 1996, when Clinton's husband, former President Bill Clinton, won re-election in a landslide.

Trump heads into the third and final debate in Las Vegas Wednesday night amid slipping fortunes, as an avalanche of sexual misconduct allegations have clouded his campaign in recent weeks. A new national poll from Bloomberg Politics found Clinton leading Trump by nine nationwide.

And as her lead as swelled nationally, Clinton has cut into Trump's support in longtime red states. A poll published Tuesday from the University of Houston showed Clinton and Trump neck-and-neck in Texas, a state that hasn't voted for a Democrat since 1976.

Read More