For the first time this year, investors are starting to get a clear look at where China’s economy really stands—and the picture isn’t pretty.

Data for January to April was as distorted as a funhouse mirror, due to changing Lunar New Year holiday dates, and a big value-added tax cut, which pulled activity forward into March from April. That allowed optimists to argue things weren’t as bad as they appeared. May is the first month since December that offers investors a clear look at where things really stand.

That...