Annual growth rose slightly from 8.5% to April, but on a monthly basis prices fell by 0.10% between April and May.
On a quarterly basis prices were 2% higher between March and May 2015 compared to December 2014 and February 2015, down from 2.6% to March on a quarterly basis.
Martin Ellis, housing economist, said: “Housing supply remains extremely tight with the stock of properties available for sale currently at its lowest level for many years.
“At the same time, ongoing economic recovery, increasing employment, real earnings growth and very low mortgage rates are all supporting housing demand.
“This combination has kept annual house price inflation well above earnings growth although activity levels are subdued.”
He added: “The imbalance between supply and demand is likely to continue to push up house prices over the coming months.
“Looking further ahead, the increasing level of house prices in relation to earnings is expected to dampen house price growth.”
House prices currently stand at £196,067 on average.
Jonathan Samuels, chief executive of Dragonfly Property Finance, said: “Housing demand, as the Halifax says, is strong — but supply appears to have gone AWOL.
"The strength of demand was certainly reinforced by the Bank of England's April mortgage approvals data, which showed a spike and suggests an increase in transactions in the months ahead.
"Demand, understandably, is being driven by the often mind-blowing rates available on mortgages today, the low cost of living and a solid jobs market.
"Unless supply improves materially, it's hard to see how prices will not continue to rise throughout 2015, albeit at a more moderate pace relative to last year.
"The denouement surrounding Greece and the Eurozone could also impact the UK economy, and therefore property market. But until the supply side problems resolve themselves, expect prices overall to continue to rise."
