* Bond yields rise after stock market-driven fall on Tuesday * Greece sells 5-year bond after rating upgrade (Updates rates) May 5 (Reuters) - Euro zone bond yields rose on Wednesday as equity markets recovered from a sudden slump a day earlier that had sent yields on the safe-haven assets falling sharply. Stock markets fell 0.5% on Tuesday in a matter of minutes and further afterwards, leaving traders perplexed as to what was behind the move. That was followed by U.S. Treasury Secretary Janet Yellen’s comments that rate hikes may be needed to stop the economy overheating as a vast stimulus programme boosts growth, which predominantly hit equity markets, but also cut the fall in bond yields. Expectations of higher growth and inflation, predominantly driven by the U.S. stimulus programme, have pushed bond yields higher on both sides of the Atlantic this year. Yellen said later that she does not anticipate inflation would be a problem for the U.S. economy and any price increases would be transitory. With European equity markets opening higher on Wednesday, bond yields, which move inversely with prices, edged up in early trade. Germany’s 10-year yield, the benchmark for the region, was up 1 basis point at -0.21% at 1500 GMT, after a brief acceleration in the rise in yields alongside U.S. Treasury yields earlier, when the U.S. Treasury refunding announcement came out. “I expect the (yield) curves in the eurozone and the U.S. to steepen, driven by better equity markets and ahead of the ADP and (non-farm payrolls) print which should be supportive for the inflationary thesis,” said Sebastien Galy, senior macro strategist at Nordea Asset Management. ADP data showed private U.S. payrolls, though slightly missing expectations, increase solidly in April and figures for March were revised upwards. Non-farm payrolls data will provide further insight on Friday. Focus in the primary market was on Greece, which received 20 billion euros of demand for a new five-year bond that will raise 3 billion euros, according to a lead manager. Greece’s deal comes after a credit rating upgrade by S&P in April, to BB. There is scope for a further upgrade given the positive outlook on the rating, now two notches below investment-grade, increasing the likelihood of Greece’s return to the investment-grade ratings it lost during its debt crisis a decade ago. Earlier, euro area April services sector PMIs showed activity in Spain expanded for the first time since July, while it continued to contract in Italy, but this had little market impact. The euro zone composite PMI, which covers both manufacturing and services, rose more than initially estimated. (Reporting by Yoruk Bahceli; Editing by Philippa Fletcher, Alex Richardson and Estelle Shirbon) Our Standards: The Thomson Reuters Trust Principles.