Year-over-year comparisons reflect the abysmal economic conditions during the pandemic. It's like comparing your current net income to one year ago but one year ago you were unemployed and paying off student loans while today you have a job at Google.
The comparisons to watch are month-over-month (MoM). The BLS reports MoM CPI increased 0.6%, after a 0.8% MoM increase in April:
https://www.bls.gov/news.release/cpi.nr0.htm
So the rate of CPI change is negative MoM.
From the same page, BLS reports CPI less food and energy fell MoM from 0.9% in April to 0.7% in May.
The real headline here should be that inflation is slowing on a MoM basis.
It's that rate of change of inflation that matters. If it remains negative (disinflation), then price increases will continue to subside.
But if CPI growth remains negative for long enough, it can translate into deflation. That's not an outcome being discussed widely now, and for that reason (among others) it should be considered seriously.
Policy makers talk and act as if only one of those two outcomes truly terrifies them: deflation. Japan has been in an on-again-off-again deflationary slump for decades, despite the BoJ now owning a good chunk of the Japanese stock market, many years of QE, and substantial deficit spending.