Washington (CNN) Donald Trump and Hillary Clinton are neck and neck in North Carolina, a state solidifying its position as a perennial presidential election battleground, while Trump holds a 5-point lead in the traditionally GOP-tilting state of Arizona, according to new CNN/ORC battleground state polls.

Trump is the choice of 43% of registered voters in Arizona , while Clinton stands at 38%, followed by Libertarian candidate Gary Johnson at 12% and Green Party nominee Jill Stein at 4%. In North Carolina , Clinton stands at 44%, Trump at 43% and Johnson at 11%. Stein will not appear on the ballot there.

Looking at the narrower pool of those likely to turn out in November, the race doesn't change significantly in either state. Trump's lead in Arizona widens slightly to 7 points, while the 1-point difference between the two candidates in North Carolina shifts to a tied race. Likely voters become a more meaningful subgroup as the election gets closer and voters settle on whether they will turn out and whom they will support.

North Carolina could be critical to Trump's campaign, given recent polling suggesting Clinton holds a wide lead in neighboring Virginia and in Pennsylvania. Should those electorally-rich states remain off the board, North Carolina's 15 votes become more important for Trump's path to victory.

The education gap among white registered voters that has been among the sharpest electoral divides in pre-election polling on this race thus far continues in both states, but it is nearly twice as wide a gap in North Carolina as in Arizona. Clinton tops Trump by 8 points among whites with college degrees in North Carolina, but Trump tops Clinton by a whopping 42 points among those whites without degrees in North Carolina, meaning the education gap there stands at 50 points. In Arizona, Trump is ahead in both groups, by a statistically insignificant 2 percentage points among those with degrees and a far wider 30 points among whites without degrees, making for a 28-point gap between the two groups.

Both North Carolina and Arizona also illustrate the challenges Trump may face in his newly launched effort to appeal to minority voters. In North Carolina, more than 20% of the electorate was black in 2012, and about 18% of Arizona voters were Latino, according to exit polls in each state.

In the new polls, Trump trails by a wide margin in both subgroups. Among blacks in North Carolina, 88% say they support Clinton, 7% Johnson and just 3% Trump. Among Hispanic voters in Arizona, 57% back Clinton, 20% Trump, 15% Johnson and 5% Stein. A key component of Trump's pitch to these groups is his claim to be able to improve their economic situation, yet in both states, non-whites broadly trust Clinton over Trump on handling the economy, with Hispanics in Arizona breaking 61% to 36% in Clinton's favor and blacks in North Carolina breaking 85% for Clinton to 12% for Trump.

There's a gender gap between Clinton and Trump in North Carolina, but women and men in Arizona are largely on the same page. Women break 48% to 40% in Clinton's favor in North Carolina, while men break 47% Trump to 40% Clinton. In Arizona, women and men both favor Trump by narrow margins, 4 points among women, 5 points among men.

Trump's lead in Arizona is also bolstered by support from independent voters, who back him by a 41% to 27% margin, with 20% behind Johnson. In North Carolina, independent voters are more evenly split, 40% Trump to 38% Clinton with 18% behind Johnson.

In both states, Trump has an edge over Clinton as more trusted to handle both the economy and terrorism, two top issues for voters nationally. Voters in both states say Clinton is better able to handle foreign policy. In Arizona, where immigration policy has been a front-and-center issue for years, Trump holds a 6-point lead as more trusted on that issue, and he also narrowly tops Clinton by 3 points on handling health care. Arizona has been deeply affected by insurers curtailing their presence in the health care exchanges created by the Affordable Care Act, also known as Obamacare, with Pinal County becoming the first in the nation where no insurers are selling their policies on the exchange there.

In North Carolina, Clinton and Trump are about even on who would better handle immigration (49% choose Trump, 47% Clinton), and Clinton has a 5-point lead on handling health care.

Clinton's position in North Carolina is bolstered by a sense that she can better handle the responsibilities that come with being commander in chief (50% trust her vs. 43% who trust Trump on that score) and that she better shares voters values (47% think Clinton does, 42% Trump). Trump tops Clinton as more honest and trustworthy (49% to 39%), and 11% say neither major party candidate for president has the edge on honesty.

In Arizona, the share who see neither as honest and trustworthy rises to 16%, and Trump continues to top Clinton on that measure (49% to 33%). The two are closer on shared values in the western battleground (44% Trump to 43% Clinton), but Clinton holds a 5-point lead as a better commander in chief. Among veterans, however, Trump tops Clinton on that in both states. In Arizona, veterans say Trump would better handle being commander-in-chief by a 56% to 35% margin; in North Carolina, it's a narrower 49% to 42%. Trump also holds an overall lead in veterans' vote preference in both places.

President Barack Obama's rising approval ratings have been a boon to Clinton nationally, though in these two states, the President's ratings remain mixed. Among registered voters in North Carolina, 49% approve and 49% disapprove, while in Arizona, they tilt toward disapproval, 51% disapprove and 46% approve. Those North Carolina marks represent an improvement for the Democratic President compared with 2014, when majorities disapproved of his work as president just before that year's midterm elections.

Both states also feature high-profile races for the Senate in addition to the presidential battle this year. In Arizona, John McCain, the former Republican nominee for president, holds healthy leads over the Republican challengers he will face in next Tuesday's primary election and over his likely Democratic opponent in November, Ann Kirkpatrick. McCain tops Kelli Ward by a 55% to 29% margin among likely Republican primary voters, while he tops Kirkpatrick by a 52% to 39% margin among registered voters.

In North Carolina, the race between incumbent Republican Sen. Richard Burr and Democratic challenger Deborah Ross is near-even; 49% of registered voters back Burr, 46% Ross. Burr holds a slightly larger 5-point lead among those likely to turn out in November. North Carolina Gov. Pat McCrory trails his Democratic challenger Roy Cooper in that race, with Cooper up 6 points among both registered and likely voters.

The CNN/ORC polls in Arizona and North Carolina were conducted by telephone August 18 through 23. In Arizona, 1,003 adults were interviewed in English or Spanish depending on the respondent's preference, including 842 registered voters. In North Carolina, the sample of 1,009 adults included 912 registered voters. The margin of sampling error for results among registered voters is 3.5 percentage points in each state.