* US dollar posts sharp gains after U.S. jobs report

* Government debt tumbles after jobs data boosts optimism

* Global stocks end mostly flat after May jobs data

* Oil slips after hitting 7-month high over $70 a barrel (Adds close of U.S. markets activity)

By Herbert Lash

NEW YORK, June 5 (Reuters) - The U.S. dollar gained sharply, and bond yields soared on Friday, but global stocks were little changed after some investors viewed news of slowing U.S. job losses in May as another sign of economic recovery.

Stock and oil prices initially rose on the much better-than-expected U.S. employment data, but after climbing to more than $70 a barrel, crude prices ended lower and stocks ended little changed.

While U.S. employers cut 345,000 jobs last month -- the fewest since September last year and far less than economists had forecast -- unemployment hit its highest rate in nearly 26 years, a reminder that the economy is far from recovery.

The unemployment rate raced to 9.4 percent, the highest since July 1983, from 8.9 percent in April.