The foreclosure listing service RealtyTrac says Ohio foreclosure filings fell sharply in May, but the state had one of the highest rates in the country. More than 87 hundred foreclosure-related documents were filed in Ohio, down 27 percent from April and 15 percent from May of last year. The state posted the third-highest foreclosure rate in the nation in May, with one in every 584 Ohio households receiving a foreclosure-related notice. Spokesperson Daren Blomquist says nationally, foreclosures rose by 11 percent last month.