If you want to understand the Egyptian uprising and how U.S. officials should respond, let me take you back to the pro-democracy demonstrations I witnessed in Cairo in 2005.

Middle-class protesters went to the streets then, too, demanding free elections. But the government of President Hosni Mubarak — tarring all opposition as radical Islamists — surrounded them with police in Darth Vader helmets and shields.

I spoke with professional women who had been beaten and groped by police, and with young women journalists whom security agents had threatened to jail on prostitution charges. I interviewed a conservative judge who was furious because the government had forbade the judiciary to monitor Egypt’s first contested presidential election. “If we had an independent judiciary and fair elections, everything would change,” I was told by Judge Hesham el-Bastawi. The judge later had a heart attack after being threatened by the regime.

I interviewed Egyptians in a working-class slum who complained bitterly about economic conditions, before a burly plain-clothes cop snatched and ripped up my notebook; he threatened to punch me when I tried to grab the notes back.

Those 2005 demonstrations were small but were a preview of today’s drama. Instead of encouraging a middle-class opposition, the regime crushed it, rigging 2010 parliamentary elections so boldly that the governing party won nearly all seats.

The current revolt is far larger, inspired by the rebellion in Tunisia. Egypt’s demonstrators are linked not by clear leadership but by cell phones, Facebook, and Twitter (which the regime blocked last Tuesday).

The source of this Egyptian revolt is not Islam, nor is it simply poverty and unemployment. “This is not only about economics,” says Marwan Muasher, a former deputy prime minister of Jordan who fought for political reforms in his country and is an astute Mideast observer.

“Most of the slogans are about governance,” Muasher says. “People are fed up with the corruption.”

Egyptian demonstrators — mostly young, often college-educated, and jobless — want a reason to hope for their future. They watch bitterly as privileged Egyptians grow rich from corrupt regime ties. They have no voice in the system and no chance of replacing a frozen governing party whose leader has held power for 29 years. That’s why they are calling for Mubarak to go.

“Until Arab leaders are willing to put countries on a sustained reform process, and to share power, things will get worse,” says Muasher, now a vice president at the Carnegie Endowment in Washington.

Serious reform, he says, means “a serious parliament, serious electoral laws, a serious political opening, with no restrictions on political parties.” He says Islamist groups, with their strong following, must be permitted to run so long as they commit to “peaceful means and peaceful rotation of power.”

If people in Egypt and elsewhere in the region could see a serious reform process put in place, “they would be willing to wait,” Muasher says. “But things like bringing sons to power are out,” he emphasizes, referring to Mubarak’s reputed plan to have his son Gamal succeed him as president.

The Obama administration has had understandable trouble figuring out a response to the uprising, for the same reasons the Bush White House backed off its early support for Egyptian democracy activists. Egypt is a vital ally in fighting Islamist terrorists and in curtailing the spread of Iranian power. Cairo has a peace treaty with Israel and has worked with Washington to curb Hamas Islamists in Gaza and push for the renewal of Israeli-Palestinian talks.

Moreover, the Egyptian revolt has no clear leadership; its titular head, former U.N. official and Nobel laureate Mohamed ElBaradei, only just returned to Egypt and has few deep links to the protesters. He is now under house arrest.

The best-organized opposition group is the Muslim Brotherhood (although it has not led this upheaval). This raises U.S. fears about a future Islamist government in the region’s largest country. A newly elected Egyptian regime might be anti-American, upending U.S. policy in the Mideast.

Yet the march of Egyptian history won’t wait. Calls by Secretary of State Hillary Rodham Clinton and President Obama for nonviolence, and their pleas for Mubarak to engage the opposition, have been outpaced by events. The United States is behind the curve.

The moderate middle-class demonstrators I met in 2005 were ready for engagement with Mubarak, but he blew it. Today’s rebels might accept a serious dialogue that led to a free vote.

But the Egyptian president isn’t listening. His appointment of a new government, and (for the first time) of a vice president, intelligence chief Omar Suleiman, won’t satisfy protesters. They want Mubarak out.

The big question now: Will Egypt’s army, which is still popular (unlike the police), mount a coup that ushers in a transitional government? That would permit time for the organization of new, non-Islamist parties and new elections within a reasonable time.

The Obama team is correct not to call openly for Mubarak’s exit. But there must be an unequivocal U.S. message conveyed to Mubarak and to his military — both publicly and privately — that the White House endorses Egyptians’ call for serious dialogue that leads to free elections.

This will not be an American diktat. The Egyptian drama will produce a new leadership sooner or later no matter the U.S. message. But a clear U.S. position might help make the transition more peaceful and put Washington on the right side.