There were 52,092 approvals in the month, compared to 52,071 approvals in April, the Australian Bureau of Statistics said on Friday.
That was better than the 0.5 per cent fall in housing finance commitments that economists were expecting.
The figures were another sign that the housing market is taking a break after a year of strong growth, said ANZ head of Australian economics Justin Fabo.
"Housing finance has flattened out at a pretty high level. It's risen substantially and now, along with building approvals, it's just taking a bit of a pause," Mr Fabo said.
"These are further signs that the housing market has cooled off a little bit.
"The level of activity - approvals, auction clearance rates - they're all still at pretty high levels relative to recent years so it's still strong, it's just not getting stronger."
He said policy makers would be pleased that the housing market was taking a bit of a breather.
CommSec economist Savanth Sebastian said housing was taking the baton from mining as the big driver of growth in the economy.
"The housing boom is cooling off but it's still going to remain relatively strong," Mr Sebastian said.
"It's going to be the big driver of growth for the Australian economy - it's supporting employment and it's supporting retail, particularly furniture and floor covering.
"It's really taken that baton from mining.
"Keep in mind also that there's a lot of construction to come with building approvals hitting record highs a couple of months back.
"It does suggest that over the next 12 months, the residential construction sector is going to be very strong."
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