* U.S. to sell $17 bln in 2-year FRN, $38 bln 5-year notes * Fed widely seen raising interest rates at policy meeting * U.S. 5-year yield touches highest level since June 2009 * U.S. 10-year, 30-year yields hit highest since May By Richard Leong NEW YORK, Sept 25 (Reuters) - U.S. Treasury yields climbed on Tuesday, with the 10-year yield hitting a four-month peak in advance of government debt supply and on bets about Federal Reserve interest rate increases in the coming months. The U.S. Treasury Department will sell $38 billion in five-year debt at 1 p.m. EDT. (1700 GMT) It will auction $17 billion in two-year floating-rate notes and $40 billion in one-month bills at 11:30 a.m. (1530 GMT) The government has ramped up borrowing since February as the deficit has grown following the massive tax cut enacted last December and a federal spending deal inked in February. Traders and analysts widely expect the U.S. central bank to lift the target range on key overnight borrowing costs by a quarter point at a two-day policy meeting that will begin Tuesday. Rates futures implied traders priced in an 80 percent chance the Fed would raise rates again in December, CME Group's FedWatch program showed. Fed officials have signaled in recent days that the U.S. economic expansion remains intact with inflation heading toward their 2 percent goal, which would allow for more rate hikes in coming months. "We're seeing risks skewed hawkishly," said Blake Gwinn, U.S. rates strategist at NatWest Markets in Stamford, Connecticut. "People have been leaning short for the past month." Expectations of rate hikes has prompted many investors to sell Treasuries, sending short-dated yields to their highest in a decade. Still, Treasuries have drawn some support from worries that global trade tensions might hurt the U.S. economy. At 10:04 a.m. (1404 GMT), the benchmark 10-year Treasury yield was 3.100 percent, up 2.2 basis points from late on Monday. Its session high of 3.113 percent was its highest since May, Reuters data showed. The 30-year yield reached 3.249 percent, its highest in four months. Five-year yield touched 2.990 percent, which was last seen in June 2009. In "when-issued" activity, traders expected the latest five-year note supply to sell at a yield of 2.983 percent , which would be the highest yield at an auction of this maturity in 10 years, according to Tradeweb. "The auction will go okay given the move (in yield) we have had," Gwinn said. September 25 Tuesday 10:05AM New York / 1405 GMT Price US T BONDS DEC8 139-24/32 -16/32 10YR TNotes DEC8 118-112/256 -6/32 Price Current Net Yield % Change (bps) Three-month bills 2.175 2.2175 0.000 Six-month bills 2.3175 2.3776 0.008 Two-year note 99-214/256 2.8351 0.008 Three-year note 99-138/256 2.9129 0.017 Five-year note 98-244/256 2.9797 0.021 Seven-year note 98-20/256 3.0597 0.023 10-year note 98-24/256 3.1001 0.022 30-year bond 95-124/256 3.2368 0.027 YIELD CURVE Last (bps) Net Change (bps) 10-year vs 2-year yield 26.30 -0.50 30-year vs 5-year yield 25.50 -0.10 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 16.75 0.25 spread U.S. 3-year dollar swap 16.25 1.25 spread U.S. 5-year dollar swap 12.75 1.00 spread U.S. 10-year dollar swap 5.75 0.50 spread U.S. 30-year dollar swap -6.75 0.50 spread (Reporting by Richard Leong; Editing by David Gregorio)