* Euro STOXX 50 rises 1.3 pct, hits 5-year high
* ECB's surprise rate cut pushed down euro, boosts exporters
* FTSEurofirst 300 also at 5-year peak, up 1.3 pct
LONDON, Nov 7 (Reuters) - A surprise rate cut by the European Central Bank sent euro zone shares to a five-year high on Thursday as traders bet a weaker euro and easier lending conditions would help revive the region's economy and boost demand for stocks.
The Euro STOXX 50 index of euro zone blue chips rose 1.3 percent to 3,095.51 points after the ECB decision, hitting a level not seen since September 2008.
The ECB was expected to leave interest rates unchanged and investors will now listen for any hint at a press conference starting at 1330 GMT that the bank may offer more cheap loans to banks next year to head off a rise in interbank lending rates.
"This will give European exporters much-needed breathing space, with the euro currency finally falling back," David Thebault, head of quantitative sales trading, at Global Equities, in Paris.
Among exporters, tyre-maker Continental rose 5.6 percent and personal goods manufacturer Adidas rose 3.9 percent, extending gains after releasing results.
Euro zone banks, which are heavily dependent on the health of the region's economy and conditions in the funding market, rose 3.4 percent
They were led by Commerzbank, up 12 percent after it reported an unexpected jump in third quarter profits.
It was the top riser on the pan-European FTSEurofirst 300 , which also hit a fresh five-year high and was up 1.3 percent at 1,313.59 points.