(Adds details of death, U.S. statement, more protests)
By Tomas Sarmiento and Deisy Buitrago
CARACAS, Feb 19 (Reuters) - A local beauty queen died of a bullet wound on Wednesday in the fifth fatality from Venezuela's political unrest, as imprisoned protest leader Leopoldo Lopez urged supporters to keep fighting for the departure of the socialist government.
College student and model Genesis Carmona, 22, was shot in the head during a protest on Tuesday in the central city of Valencia, and died in a clinic.
"How long are we going to live like this? How long do we have to tolerate this pressure, with them killing us?" a relative, who asked not to be named, told Reuters.
"She only needed one more semester to graduate," he added of Carmona, who had been studying tourism and had won the 2013 Miss Tourism competition in her state.
Tensions have risen in Venezuela since Lopez, a 42-year-old Harvard-educated economist, surrendered to troops on Tuesday after spearheading three weeks of often rowdy demonstrations against President Nicolas Maduro's government.
"Today more than ever, our cause has to be the exit of this government," he said, sitting next to his wife in a pre-recorded video to be released if he was arrested. (http://t.co/uJGiXVm0AV)
"The exit from this disaster, the exit of this group of people who have kidnapped the future of Venezuelans is in your hands. Let's fight. I will be doing so."
As well as the death in Valencia, three people have been shot dead in Caracas and another person run over by a car during a demonstration in the coastal town of Carupano.
There have been scores of arrests and injuries.
TROUBLE AROUND NATION
There was sporadic trouble across Venezuela again on Wednesday. Rival groups scuffled outside the Caracas court where Lopez was due, while student demonstrators also blocked a highway in the capital, burning trash.
In western Tachira state, security forces and protesters fought in the streets for about two hours, with two students injured, various vehicles damaged or destroyed, and local monuments charred, witnesses said.
In southern Puerto Ordaz city, pro- and anti-government marchers fought in the street, witnesses said, with police firing teargas to quell the trouble.
Three government supporters were injured in the melee where shots were fired, and both sides faced off with sticks and stones, the witnesses said.
The demonstrators are calling for Maduro's resignation over issues ranging from inflation and violent crime to corruption and product shortages.
Maduro, who was narrowly elected last year to replace Hugo Chavez after his death from cancer, says Lopez and others in league with the U.S. government are seeking a coup against him.
Street protests were the backdrop to a short-lived ouster of Chavez for 36 hours in 2002, before military loyalists and supporters helped bring him back.
Though tens of thousands joined Lopez on the streets when he turned himself in on Tuesday, the protests so far have mainly been much smaller than the wave of demonstrations a decade ago.
There is no evidence the military, which was the decisive factor in the 2002 overthrow, may turn against Maduro now.
Lopez was being held on Wednesday at the Ramo Verde jail in Caracas, and was due at a first court hearing.
Hundreds of supporters stood outside the tribunal, holding banners saying "Free Leopoldo!" as a line of soldiers stood in front with riot shields and gas-cannisters. "We're prepared to give our lives," said pensioner Juan Marquez, 68.
Police held back a rival demonstration by several hundred 'Chavistas', some of them striking the protesters and shouting "downtown Caracas belongs to revolutionaries".
Waving pictures of Maduro and Chavez, they chanted "Leopoldo, off to Tocoron" in a reference to a notoriously overcrowded provincial jail.
In an intriguing twist to the drama, Maduro said his powerful Congress head Diosdado Cabello, seen by many Venezuelans as a potential rival to the president, personally negotiated Lopez's surrender via his parents.
Cabello even helped drive him to custody in his own car given the risks to Lopez's life from extremists, Maduro said.
With local TV providing minimal live coverage of the street unrest or opposition leaders' news conferences, Twitter, Instagram and Facebook have become the go-to media for many Venezuelans desperate for information on the crisis.
However, many social media users are indiscriminately tweeting images without confirming their origin, leading to manipulation and gaffes including footage of unrest in Egypt and Chile being passed off as repression in Venezuela.
Old photos from past protests are also doing the rounds.
Detractors call Lopez a dangerous and self-serving hothead. He has frequently squabbled with fellow opposition leaders, and was involved in the 2002 coup, even helping arrest a minister.
"I've hardly been in office for 10 months and for 10 months this opposition has been plotting to kill me, topple me," Maduro said. "For how long is the right wing going to hurt the nation?"
Though the majority of demonstrators have been peaceful, a radical fringe have been tossing stones at police, blocking roads and vandalizing buildings.
Rights groups say the police response has been disproportional, with some detainees tortured.
In a nation split largely down the middle on political lines, 'Chavistas' have stayed loyal to Maduro despite unflattering comparisons with his famously charismatic predecessor. Many Venezuelans fear the loss of popular, oil-funded welfare programs should the socialists lose power.
Maduro expelled three U.S. diplomats this week, accusing them of recruiting students to protest. Washington said on Wednesday it was considering reciprocating. (Additional reporting by Andrew Cawthorne and Diego Ore in Caracas; Javier Farias in Tachira; German Dam in Puerto Ordaz; Writing by Andrew Cawthorne; Editing by Chizu Nomiyama)