(Recasts with services sector data, adds factory orders, updates markets)
* ISM services sector index falls 0.6 percentage point in May
* Factory orders slip 0.2 percent in April
* First-quarter productivity revised up to show it unchanged
* Growth in unit labor costs revised down to 2.2 percent rate
WASHINGTON, June 5 (Reuters) - U.S. services sector activity slowed in May as new orders tumbled, but a jump in employment to a near two-year high pointed to sustained labor market strength despite a deceleration in job growth last month.
Other data on Monday showed orders for manufactured goods fell in April for the first time in five months, while worker productivity was unchanged in the first quarter.
The Institute for Supply Management (ISM) said its non-manufacturing activity index fell six-tenths of a percentage point to a reading of 56.9. A reading above 50 indicates expansion in the sector, which accounts for more than two-thirds of U.S. economic activity.
Services industries reported a 1.7 percentage points drop in production last month and new orders tumbled 5.5 percentage points. But a measure of services sector employment surged 6.4 percentage points to 57.8, the highest reading since July 2015.
The government reported on Friday that the economy added 138,000 jobs last month after creating 174,000 positions in April. U.S. stocks were trading higher, while the dollar edged up against a basket of currencies. Prices for U.S. Treasuries fell.
The Federal Reserve is expected to increase borrowing costs at its June 13-14 policy meeting. The U.S. central bank raised its benchmark overnight interest rate by 25 basis points in March.
In a separate report on Monday, the Commerce Department said factory goods orders dropped 0.2 percent in April after jumping 1.0 percent in March. Factory orders were up 4.4 percent from a year ago.
Manufacturing, which accounts for about 12 percent of the U.S. economy, is being supported by a recovery in the energy sector that has led to demand for oil and gas drilling equipment. A manufacturing survey last week showed a measure of factory activity steady in May after two straight months of declines.
The Commerce Department also showed orders for non-defense capital goods excluding aircraft - seen as a measure of business confidence and spending plans - edging up 0.1 percent instead of being unchanged as reported last month.
Shipments of these so-called core capital goods, which are used to calculate business equipment spending in the gross domestic product report, nudged up 0.1 percent instead of the previously reported 0.1 percent decrease.
A third report from the Labor Department showed nonfarm productivity, which measures hourly output per worker, was unchanged in the last quarter. It was previously reported to have declined at a 0.6 percent annualized pace.
The government also reported that the growth in labor costs at the start of the year was not as strong as reported in May, which could cast doubts on the tightening labor market's ability to unleash robust wage growth.
The revision to first-quarter productivity was in line with economists' expectations. Productivity increased at an unrevised 1.8 percent pace in the fourth quarter.
Productivity has increased at an average annual rate of 0.6 percent over the last five years, below its long-term rate of 2.1 percent from 1947 to 2016, indicating that the economy's potential rate of growth has declined.
That suggests the Trump administration could struggle to achieve its 3 percent annual gross domestic product growth target. The economy grew at a 1.2 percent pace in the first quarter. It grew 1.6 percent in 2016 and annual GDP growth has not exceeded 2.6 percent since the 2007-09 recession ended.
Economists blame low capital expenditure, which they say has resulted in a sharp drop in the capital-to-labor ratio, for the weakness in productivity. There are also perceptions that productivity is being inaccurately measured, especially on the information technology side.
(Reporting by Lucia Mutikani; Editing by Andrea Ricci)