At the same time, elevated mortgage rates are crimping affordability.
But the data still show moderating consumer demand from the past year.
New research and commentary from officials and economists suggest the link between wages and prices may not be so direct.
The data highlights a labor market that, while largely resilient, may be starting to show signs of cooling.
Even though labor demand has remained resilient, it's unclear how long that will last.
The increase in May hiring was led by leisure and hospitality.
More than half of consumers felt that the government is doing a poor job with economic policy, the highest share in ten months.
Some economists have been wary about drawing strong conclusions from the data.
Seven out of 13 retail categories rose last month, according to Commerce Department data.
The data may bolster chances that the Federal Reserve will pause its run of interest-rate hikes.