The National Association of Realtors (NAR) reports that the seasonally adjusted annual rate of existing home sales in May rose 4.2% to 5.18 million from an unrevised total of 4.97 million in April. Sales are up 12.9% year-over-year for the month. May sales of existing homes were the highest since the tax credit period of November 2009, when sales peaked at 5.44 million.

Housing inventory rose again in May, up 3.3% to 2.22 million homes, which is equal to a supply of 5.1 months, compared with a 5.2-month supply in April. Listed inventory is down 10.1% year-over-year, when there was a 6.5 month supply available.

According to the NAR, the national median existing home price in May was $208,000, up from $192,800 in April and up 15.4% compared with May 2012. That marks the 15th consecutive month to see a price gain and the sixth consecutive month of double-digit increases. The last time housing prices went on such a string of price increases was the period between March 2005 and May 2006.

NAR’s chief economist said:

The housing numbers are overwhelmingly positive. However, the number of available homes is unlikely to grow, despite a nice gain in May, unless new home construction ramps up quickly by an additional 50 percent. The home price growth is too fast, and only additional supply from new homebuilding can moderate future price growth.

Foreclosed and short sales accounted for 18% of May sales, unchanged compared with April sales and below the 25% share in May 2012. Foreclosures sold at an average 15% discount to the May median price, while short sales sold at a discount of 12%. Both discounts decreased slightly month-over-month.

Existing, non-distressed homes were on the market for an average of 41 days, while foreclosed homes were on the market for an average of 43 days and short sales took a median of 79 days to sell.

Inventory shortages are driving prices for existing homes higher, and combined with rising mortgage loan rates, the pace of home sales is slowing. As the NAR’s economist suggests, new construction is needed — and it is coming, but building new homes takes time.

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