Nationwide report showing property prices have risen by 11.1% over the last year also marks the second month in a row where annual growth in property values has hit double digits, following a 10.9% year-on-year uplift in April.
But on a monthly basis, prices rose by 0.7% in May, which represents a slowdown compared with the 1.2% monthly increase seen in April.
Property values have now been edging up for 13 months in a row on a month-on-month basis. Across the UK, average house prices now stand at £186,512.
Robert Gardner, Nationwide's chief economist, said it is "too early" to say whether the housing market is seeing the start of a cooling trend.
Mr Gardner said some signs of a slowdown may partly be due to toughened mortgage lending rules introduced in April, "which may take a few months to bed down".
More top news
Sex and drugs are off limits for undercover police, official guidelines published for the first time state.
Nicola Sturgeon will hold talks with European Parliament president Martin Schulz in Brussels today.
IKEA is recalling almost 36 million chests and dressers in the US and Canada after the deaths of three children.