HSBC
Russia's HSBC composite output index fell to a four-month low of 47.6, down from 48.9 in April.
A PMI above 50 signals growth, while a number below 50 signals a contraction.
"The stuttering nature of Russia's manufacturing sector continued to May, with a rather disappointing set of survey data," said Paul Smith, Senior Economist at Markit.
The biggest takeaways from May's survey are that output fell following an accelerated reduction in new work, and that there were job cuts amid signs of excess capacity.
"However, the contraction remains primarily centered on the investment goods sector, while the ongoing trend towards price level stabilization suggests the macroeconomic environment is showing some sign of improvement. This could, in time, help the manufacturing economy regain some lost ground over the coming months," Smith added.
Plus, manufacturers "benefited to some degree" from the ruble's stabilization against other the dollar and euro, and inflation rates continue to fall.
But overall, this latest manufacturing survey suggests that even with lower inflation and a stronger ruble, lower oil and Western sanctions are still affecting Russia's economy.