* MSCI world share index at highest since 2008, DAX at record high * German data lifts euro, possible ECB action caps gains * Aussie dollar falls on RBA rate cut NEW YORK, May 7 (Reuters) - World stock indices hit their highest levels in almost five years on Tuesday, with the German benchmark joining the S&P 500 at a record high after unexpectedly strong data amid signs top central banks will remain supportive of growth. Wall Street edged up at the open, with the S&P touching an intraday high of 1,623.74. Recent gains in U.S. equities have come on strength in technology, basic materials and banking shares, sectors that are closely related to an economy in expansion. "If this rotation into cyclical stocks from defensive ones continues, that will be a very healthy sign for us," said Art Hogan, managing director at Lazard Capital Markets in New York. He said, however, that Wall Street could drift along this week with little in the U.S. data calendar to give direction. "All the recent catalysts have been priced in and markets are at a level they're comfortable with," Hogan said. In morning trading in New York, the Dow Jones industrial average was up 33.25 points, or 0.22 percent, at 15,002.14. The Standard & Poor's 500 Index was up 2.84 points, or 0.18 percent, at 1,620.34. The Nasdaq Composite Index was down 2.53 points, or 0.07 percent, at 3,390.44. MSCI's global index, which tracks stocks in 45 countries, edged past its June 2008 high in Asian trading after Japan's stock market, which had been closed on Monday, soared in a delayed reaction to Friday's strong U.S. jobs data. The global index was up 0.4 percent at 372.60. The momentum continued in Europe, where the DAX hit a record as German industrial orders for March rose 2.2 percent from February, beating a forecast of a 0.5 percent drop on strong demand from the euro zone. With key economies like the United States seeing a patchy recovery but others struggling to maintain growth, major central banks around the world have shown over the last few weeks they intend to keep stimulus flowing freely for the time being. Australia's central bank cut rates to a low of 2.75 percent on Tuesday and suggested it may ease further. The move followed European Central Bank chief Mario Draghi saying on Monday that the ECB was ready to trim rates again if needed, after a rate cut last week. The growth-linked Aussie dollar was last at US$1.0173, down 0.7 percent on the day. Draghi's comments that the ECB could cut rates, including pushing its deposit rate into negative territory, kept downward pressure on the euro, although the stronger German data pushed it back near $1.31, up 0.2 percent on the day. Spanish and Italian bond yields - a proxy for borrowing costs - were both slightly lower while safe-haven German Bund yields were at a three-week high. U.S. Treasuries yields rose to three-week highs as traders prepared for the sale of $32 billion in new 3-year notes. Benchmark 10-year note yields rose to 1.78 percent, up from 1.76 percent on Monday and the highest since April 12. Many analysts see yields as unlikely to march significantly higher from unless there are new signs that the economic recovery is not slowing as much as feared. "One decent number is not strong enough to completely change the mood of market players," said Jason Rogan, managing director of Treasuries trading at Guggenheim Partners in New York. "We're getting close to a point where you might start to see some buying." Prospects the U.S. economy will lead global growth lifted industrial commodities, although persistent worries about demand from top consumers such as China tempered gains. Three-month copper hit a three-week high of $7,374 a ton but then fell 0.4 percent a day after its largest daily percentage gain since October 2011. Copper prices are almost 9 percent lower for the year. Brent crude oil prices edged up, supported by strong German data, central bank policy and tension in the Middle East. Oil rose in Monday as Israeli air strikes on Syria escalated tensions in the Middle East, trumping worries about global demand. Brent was last up 0.1 percent at $105.58 while U.S. crude shed 0.3 percent to $95.85.