* C$ at C$1.0055 vs US$, or 99.45 U.S. cents * Currency hits strongest since Feb. 15 vs greenback * Global stocks strongest in five years * C$ surges against Aussie as RBA cuts rates * Bond prices mostly lower By Andrea Hopkins TORONTO, May 7 (Reuters) - The Canadian dollar strengthened to a 2-1/2-month high against its U.S. counterpart on Tuesday as shares globally hit their strongest level in almost five years and top central banks signaled they will remain supportive of growth. MSCI's global index, which tracks stocks in 45 countries, edged past its June 2008 highs in Asian trading after Japan's Nikkei stock market, which had been closed on Monday, jumped in a delayed reaction to Friday's U.S. jobs data. The momentum continued in Europe, where the DAX hit a record following strong industrial data. The head of the European Central Bank had underpinned the positive mood on Monday by saying the ECB was ready to trim rates again if needed, while the Reserve Bank of Australia cut rates to a new low of 2.75 percent on Tuesday and suggested it may do more. "The Canadian dollar is being held up by some of the crosses -- particularly the Aussie-CAD ... in the backwash of the RBA move, and that has provided a reasonably healthy backdrop for the Canadian dollar overall," said Jeremy Stretch, head of foreign exchange strategy at CIBC World Markets in London. At 9:28 a.m. (1328 GMT), the Canadian dollar was trading at C$1.0055 to the U.S. dollar, or 99.45 U.S. cents, stronger than Monday's North American close at C$1.0068 to the U.S. dollar, or 99.32 U.S. cents. The currency at one point touched C$1.0036 against the greenback, its strongest level since Feb. 15. The Canadian dollar rallied to its strongest level since October against Australia's currency after the RBA surprised many traders with the rate cut. The Canadian dollar firmed as far as C$1.0211 to the Australian currency. Stretch said the Canadian dollar was likely to be range-bound for most of the session against the U.S. dollar, finding support if it weakened toward C$1.0080 to C$1.0095, while strength would be limited to C$1.0050 or parity with the U.S. dollar. He said traders would be watching data on Canadian housing starts, due to be released on Wednesday. The report is expected to show the pace of new homebuilding to slow to a seasonally adjusted annual rate of 175,000 units in April, down from 184,000 units in March. Investors are also awaiting Friday's Canadian employment data. The report is expected to show the economy added 15,000 jobs in April, while the unemployment rate held steady at 7.2 percent, according to a Reuters survey of analysts. Traders are also looking for more clues on what newly appointed Bank of Canada Governor Stephen Poloz will say about monetary policy. Prices for Canadian government bonds were mostly lower. The two-year bond fell 1.3 Canadian cents to yield 0.984 percent, while the benchmark 10-year bond fell 22 Canadian cents to yield 1.826 percent.