* Dollar index hits lowest since Oct. 13
* Euro rises to highest in nearly 2 months (Updates to U.S. market open, adds quote, changes dateline, previous LONDON)
NEW YORK, Nov 24 (Reuters) - The dollar fell to a five-week low against a basket of currencies on Friday as investors grew optimistic about the strength of the euro zone's recovery and lost appetite for the greenback.
The single currency hit its highest since Sept. 25, up 0.25 percent on the day and nearly 0.75 percent for the week. It would be the euro's third straight week of gains against the dollar, its best run since July.
"You had good data (this week) from Europe, pretty good news from Germany and nobody guarding the dollar as were all eating turkey," said John Doyle, director of markets at Tempus Inc in Washington.
On Thanksgiving Thursday, while markets in the U.S. were closed, euro zone business growth surveys showed surprise growth, supporting the European Central Bank's move last month to announce a throttling back of its monetary stimulus.
The currency bloc has emerged as the surprise economic star of 2017 and future-looking indicators in the latest Purchasing Managers' Index (PMI) suggest the upturn still has momentum.
The dollar index fell to its lowest since Oct. 13 at 92.876, having suffered its worst single-day decline in more than five months on Wednesday after minutes from the Federal Reserve's latest policy meeting showed some policymakers concerned about stubbornly weak U.S. inflation.
The core personal consumption expenditures price index has consistently fallen short of the central bank's 2 percent target for over five years, even as the Fed has moved toward normalizing policy.
"Theres an underlying medium-term trend here taking shape towards a weaker dollar," said BMO Capital Markets currency strategist Stephen Gallo, in London.
"When you have firm global risk appetite, pretty firm global growth conditions including in the euro zone, and firm global commodity prices, there isnt a lot of if any safe-haven demand for dollars," he said.
Gallo added that developments in Germany, where the Social Democrats (SPD) appear close to dropping their opposition to renewing cooperation with Chancellor Angela Merkel, was giving some added support to the euro.
Minutes from the European Central Bank's latest policy meeting, released on Thursday, showed policymakers had broadly agreed on extending their quantitative easing (QE) scheme, albeit at a lower level, though a decision to keep the asset purchases open-ended appeared to generate fiercer debate.
The euro makes up more than 50 percent of the dollar index's weight.
Sterling rose to its highest against the dollar since Oct. 2 as markets interpreted the latest comments from top European Union policymakers as mildly positive for Brexit negotiations.
(Reporting by Dion Rabouin; Additional reporting by Jemima Kelly; Editing by Susan Thomas)