WASHINGTON (CNN) — Could Barack Obama’s great week mark a turning point in his poll numbers?

After months of stagnant approval ratings, a new CNN/ORC poll finds that for the first time in more than two years, 50% of Americans approve of the way Obama is handling the presidency. And his overall ratings are bolstered by increasingly positive reviews of his treatment of race relations and the economy.

The new poll follows a week in which two Supreme Court cases boosted the president’s legacy by upholding the government subsidies at the heart of Obama’s health care law, the Affordable Care Act, and affirming same-sex couples’ right to marry. All this while Obama took several opportunities to directly address the nation’s racial tensions, closing out the week by singing “Amazing Grace” on national television.

The new poll shows Obama’s approval rating up five points since a May survey, when just 45% approved of the job he was doing as president and 52% disapproved. The poll marks the first time his approval rating has been at 50% or higher since May, 2013, and only the second time in that stretch that his disapproval rating has fallen below 50%. It currently stands at 47%.

Obama’s approval rating for handling the economy has also climbed, 52% approve in the new poll, compared with 46% who approved in the May survey. That’s the first time approval for Obama’s handling of the economy has topped 50% in CNN/ORC polling in nearly six years.

A majority also approve of the President’s handling of race relations, an issue that has grown in prominence amid protests and riots following the deaths of several African-American men at the hands of police officers, and the racially motivated shooting of nine African-American churchgoers by a white man during a Bible study session in Charleston in mid-June. The poll finds 55% approve, while 42% disapprove, up from 50% who approved in the May survey.

But to sustain those numbers, the poll suggests Obama will need to overcome a growing sense that race relations are a serious problem and have worsened during his time in office.

Overall, 74% of Americans say racial discrimination against African-Americans in the U.S. is a very or somewhat serious problem, up from 57% saying so five years ago. Among African-Americans, 80% now describe this as a very serious issue, up from 42% five years ago.

And African-Americans are more likely than they were 12 years ago to say they frequently face discrimination because of their race. Forty-five percent say they face discrimination in public or at their jobs once a month or more, including nearly a quarter (24%) who say they face discrimination daily. In a 2003 CNN/USA Today/Gallup poll, 39% of African Americans said they faced discrimination at least monthly.

A plurality of all Americans now say that relations between African-Americans and whites have gotten worse in the time since Obama became president: 43% think so, while about half as many, 20%, say things have improved. Among African-Americans, opinions are evenly split, with 35% saying things have worsened while 33% think they’ve gotten better. Whites tilt toward worse: 47% say relations between African-Americans and whites have gotten worse since Obama took office.

Obama’s numbers themselves reflect the nation’s sharp divides along racial lines. While 91% of African-Americans say they approve of Obama’s handling of the presidency, just 39% of whites do, a 52-point gap. Obama’s approval rating among whites hasn’t been above 50% since 2009, while his approval rating among African-Americans has rarely dipped below 80%.

When faced with racist views or opinions, most Americans say they would be likely to challenge those views. About 6-in-10 would be very likely to challenge a close friend expressing racist views or opinions, though fewer, 45%, would be willing to challenge a stranger in the same situation.

A small number, 28%, say the shootings in Charleston, carried out by a 21-year-old white man who shared his white supremacist views online, have made them more likely to challenge someone who is expressing racist views or opinions. But 67% said the shootings haven’t changed how they would react.

Obama’s eulogy Friday of the Reverend Clementa Pinckney, killed in the Charleston shooting, also addressed gun control. The poll finds the public less receptive to Obama’s endeavors on this issue, even as support for stricter gun control has inched up following the shooting.

Just 42% of Americans approve of Obama’s handling of gun policy and 53% disapprove. That’s an improvement for Obama since spring 2014, when just 33% approved of Obama’s handling of gun policies, but slightly worse than the 46% who approved about a month after the shooting at an elementary school in Newtown, Connecticut.

Liberals and Democrats are less apt to say they approve of the way the President is handling gun control than they are on issues such as the economy or race relations. But their reviews are improving from the spring 2014 low, rising 16 points among Democrats and 13 points among liberals.

Overall, Americans are divided on whether the country should have stricter gun laws, 49% say they should be stricter, 49% oppose that. That’s a shift in favor of stricter gun laws compared with last fall, when 44% said they favored those laws.

Still, most Americans doubt that strengthening the nation’s gun laws would reduce the amount of violence or number of gun-related deaths in the U.S. Just 4-in-10 Americans say stricter laws would reduce those numbers.

More broadly, just 35% of Americans think government and society can take effective action to prevent shootings like the one in Charleston from happening again, 64% say such shootings will happen regardless of what the government does. That’s a bit more pessimistic than in December 2012 following the shootings in Newtown, when 46% thought government action could help prevent future incidents. On this question, at least, the new poll finds racial unity, with more than 6-in-10 whites and blacks alike saying action won’t help.

Many White House observers noted the week, packed with victories for Obama on the 2010 health care law and fast-track authority for trade deals, then punctuated Friday with his call to action on race relations and open celebration of a gay rights milestone he’d publicly opposed until 2012, marked a change in tone for Obama.

After all that, 50% of Americans said they think Obama is more likely to spend the final year and a half of his presidency taking advantage of the opportunity to address important problems facing our country, while slightly fewer, 46%, think he is more likely to let those opportunities pass by. Looking back over his last six and a half years in office, 47% say that so far, he’s done more to take advantage of the opportunities to address important problems, 45% that he’s wasted those opportunities.

The CNN/ORC poll was conducted June 26-28 among a random national sample of 1,017 adults. Additional interviews were conducted with African-Americans and combined with those reached through the initial sample of 1,017 for a total of 303 non-Hispanic African-American respondents. The margin of sampling error for all adults is +/- 3 percentage points, for results among African-Americans it is +/- 5.5 percentage points. Results among the 727 non-Hispanic whites reached in the initial sample have a margin of sampling error of +/- 3.5 percentage points.

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