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* Energy shares rise as oil prices gain
* Apple supplier Skyworks gains on upbeat Q2 results
* U.S. service sector activity contracts in April-ISM
* Indexes up: Dow 1.56%, S&P 500 1.60%, Nasdaq 1.85% (Adds comments, updates prices)
By Medha Singh and Shreyashi Sanyal
May 5 (Reuters) - Wall Street's main indexes jumped on Tuesday as a recovery in oil prices lifted battered energy stocks and a slew of countries eased coronavirus-induced restrictions in an attempt to revive their economies.
Some hard-hit countries, including Italy, as well as a handful of U.S. states are tentatively easing stay-at-home orders this week, raising hopes for a recovery in oil demand.
All the major S&P 500 sub-indexes were trading higher, with the energy sector rising 2.3%, but the index is still the top loser across sectors with a 35% decline this year.
Market-leading growth stocks such as Microsoft Corp , Amazon.com Inc and Apple Inc rose for a second day, helping offset concerns about the latest U.S.-China spat over the origin of the novel coronavirus.
The S&P 500 has climbed about 30% from its March lows on the back of unprecedented stimulus measures and signs of a plateau in new COVID-19 cases in many parts of the world.
"We are in the hope mode regarding the rebound that will come once the economies reopen," said Jim McDonald, chief investment strategist for Northern Trust in Chicago.
However, many market experts have warned the rally could be tested amid a risk of another wave of virus infections and with growing evidence of the damage to the economy and corporate America.
Data on Tuesday showed the domestic services sector recorded its first contraction in nearly 10-1/2-years, while the Institute for Supply Management's (ISM) non-manufacturing index showed a smaller-than-expected decline.
All eyes will now be on the Labor Department's report of monthly nonfarm payrolls due Friday.
"It's all about the mood swings and hopes of the economies reopening. But the problem is this could change once we get to see some of the hard numbers, especially the employment report," said Peter Cardillo, chief market economist at Spartan Capital Securities in New York.
With more than half of the S&P 500 companies reporting so far, first-quarter earnings are expected to have fallen 12.5%, with analysts expecting an earnings recession by the second quarter, according to Refinitiv data.
At 11:23 a.m. ET the Dow Jones Industrial Average was up 370.42 points, or 1.56%, at 24,120.18, the S&P 500 was up 45.55 points, or 1.60%, at 2,888.29 and the Nasdaq Composite was up 160.93 points, or 1.85%, at 8,871.65.
Apple supplier Skyworks Solutions Inc jumped 5.9% after reporting upbeat quarterly results, but warned of a hit from the pandemic in the current quarter.
Pfizer Inc rose 3% after announcing that a venture with its German partner had started delivering doses of its experimental coronavirus vaccines for human testing in the United States.
Advancing issues outnumbered decliners by a 3.74-to-1 ratio on the NYSE and by a similar ratio on the Nasdaq.
The S&P index recorded six new 52-week highs and no new low, while the Nasdaq recorded 38 new highs and four new lows. (Reporting by Medha Singh and Shreyashi Sanyal in Bengaluru; Editing by Anil D'Silva, Saumyadeb Chakrabarty and Shounak Dasgupta)