* China factory activity improves but still contracting
* Flash PMI shows new export orders jump, but jobs weaken
* HSBC sees some signs of stabilisation in economy
* Japan shows similar trend, but export orders weaken (Wraps Chinese and Japanese PMIs, adds comments and details)
By Koh Gui Qing
BEIJING, May 22 (Reuters) - China's factory sector turned in its best performance this year in May but still contracted for the fifth straight month, a survey showed on Thursday, with divergent signals on exports and jobs pointing to an uncertain outlook for the economy.
A similar survey showed Japanese factories had contracted slightly in May but at a slower pace than in April, suggesting some recovery from the impact a sales tax increase last month.
The HSBC/Markit Flash China Manufacturing Purchasing Managers' Index (PMI) rose to 49.7 in May from a final reading of 48.1 in April to be at its highest since December.
The first reading of China's economy in May was much stronger than the median forecast of 48.1 in a Reuters' poll, but, hovering just below the 50-point level that separates growth from contraction, it showed a slight drop in business.
That was still welcomed by those looking for signs of stabilisation after a run of weaker-than-expected data this year, and the news lifted Asian stocks and the Australian dollar -- a favourite market proxy for China's economic health.
"Looking at China as well as Japan, the Asian manufacturing business cycle could be stabilising a bit in May after a tough April, but the improvement is modest," said Bill Adams, an economist at PNC Financial.
A breakdown of China's PMI showed the handful of closely-watched indices that measure output, domestic and foreign demand in the world's second-biggest economy all recovered sharply in May to rise back above 50 points.
New export orders had the biggest turnaround, climbing a hefty 3.4 points to 52.7, a level not seen since late 2010.
Yet parts of the PMI report were also cause for concern.
The employment index fell more than one point to be well under 50, the 13th consecutive month that jobs were lost in the manufacturing sector.
A deteriorating labour market would worry the government, as jobs growth is seen as important for social stability.
Premier Li Keqiang said in March that it was acceptable for economic growth to be slightly below the 7.5 percent target this year as long as the job market held up. Previously, he has said growth of least 7.2 percent was needed to create sufficient jobs.
For now though, Julian Evans-Pritchard from Capital Economics in Singapore said Beijing needn't be too worried.
He said rising domestic infrastructure investment and export sales were offsetting the drag from sectors such as the cooling property market, where prices rose at their slowest annual pace in 11 months in April.
"While downward pressure on the economy remains, we aren't seeing as rapid a slowdown this quarter as last," he said.
Japanese manufacturing activity also contracted in May but at a slower pace, in a sign of a tentative recovery after a sales tax hike in April led to a slowdown in consumer spending.
The Markit/JMMA flash Japan Manufacturing Purchasing Managers Index rose to a seasonally adjusted 49.9 in May from a April's final reading of 49.4.
Unlike China, however, the measures for output, new orders and new export orders all fell in May. The index for new export orders fell to 48.2 from April's final reading of 49.1.
Exports have been a soft spot for the recovering economy, and policymakers have been counting on a rebound in shipments to offset the expected drop in consumer consumption in the immediate months after the sales tax increase.
But there is growing evidence that any damage from the tax hike will be limited. A Reuters survey showed companies expect sales to bounce back and are more willing to raise wages.
A slightly more upbeat assessment from the Bank of Japan on Wednesday, when it kept its policy steady, is also supporting expectations that Asia's second-biggest economy is improving, the mixed PMI report notwithstanding.
"Japan's economy is contracting in the second quarter, but isn't bad enough to push the Bank of Japan to intensify its stimulus program," said PNC's Adams. (Reporting by Koh Gui Qing; Editing by Kim Coghill and John Mair)