(Updates to late afternoon trading)
* U.S. markets mixed after July 4 holiday
* Investors see murky message in Federal Reserve minutes
* Oil tumbles on output concerns, strong dollar
NEW YORK, July 5 (Reuters) - Oil prices fell sharply on Wednesday after their longest rally in more than five years while the dollar was higher and Treasury yields were near recent peaks after minutes from the U.S. Federal Reserve's last meeting showed contrasting opinions.
Tumbling oil prices put pressure on the energy sector, which limited gains for Wall Street's S&P 500 benchmark.
Federal Reserve policymakers were split on the outlook for inflation and how it might affect the future pace of interest rate rises, according to the minutes of the Fed's June policy meeting released on Wednesday.
Investors had hoped for insight on the central bank's plans for interest rate hikes or possible balance sheet reduction.
"I see a murky, opaque message," Stephen Massocca, senior vice president at Wedbush Securities in San Francisco, said of the Fed minutes.
Trading was also affected on Wednesday by lighter participation the day after the U.S. July 4 Independence Day holiday and ahead of the U.S. jobs report due on Friday.
The Dow Jones Industrial Average fell 1.58 points, or 0.01 percent, to 21,477.69, the S&P 500 gained 3.11 points, or 0.13 percent, to 2,432.12 and the Nasdaq Composite added 36.37 points, or 0.6 percent, to 6,146.43.
U.S. Treasury yields were near multi-week or multi-month peaks after the minutes.
While he described the Fed headlines as dovish, Aaron Kohli, interest rate strategist at BMO Capital Markets in New York, said the details in the minutes were hawkish.
Benchmark 10-year Treasury notes last rose 6/32 in price to yield 2.3267 percent, from 2.346 percent.
Analysts said yields remained near their recent highs due to the possibility that Friday's U.S. non-farm payrolls report would show a jump in jobs growth in June, which would also push yields higher.
The dollar edged up against a basket of currencies and was last up 0.1 percent. It briefly pared gains after the Fed minutes.
U.S. crude fell 4.29 percent to $45.05 per barrel in its sharpest fall in almost a month and Brent was last at $47.73, down 3.79 percent on the day. Oil had risen for eight straight sessions before Wednesday.
"If you see oil dip from here and head below the mid-$40 range, it'll drag the (stock) market," said Randy Frederick, vice president of trading and derivatives for Charles Schwab in Austin, Texas. Frederick. "It's right on the threshold where if it goes lower, it'll hurt the market."
The South African Rand fell 1.7 percent against the dollar after reports the ruling African National Congress party agreed the central bank should be nationalized and President Jacob Zuma said land expropriation without compensation should be allowed where "necessary and unavoidable."
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2 percent, erasing some of Tuesday's losses, when North Korea fired a missile into Japanese waters. MSCI's gauge of stocks across the globe gained 0.15 percent.
(Reporting By Sinead Carew; Additional reporting by Sam Forgione and Richard Leong in New York, and Patrick Graham in London; Editing by Dan Grebler)