The increase in sales follows a fall in April which saw sales slump to their lowest level so far in 2017, at 22,546.
The figures revealed 481 were residential sales in for £1m and over, 304 of which were in the Capital.
The most expensive residential sale in May 2017 was a detached property in Kensington and Chelsea for £37m. The cheapest residential sale in May 2017 was of a terraced property in Wingate, County Durham for £10,250.