The quake, with a magnitude 8.0, struck at 01:12 GMT near the Santa Cruz islands, the US Geological Survey said.
A tsunami measuring 0.9m (3ft) then hit Lata on eastern Santa Cruz island, swamping the island's airport.
The worst of the damage was said to have been on the western coast of Santa Cruz, with one report putting the waves there at 1.5m.
Medical staff at Lata hospital said five people had been killed - four elderly people and one young boy.
But director of nursing Augustine Pilve told New Zealand television that number could rise.
"It's more likely that other villages along the coast of Santa Cruz may be affected," he said.
Robert Iroga, press secretary to the Solomons prime minister, told the BBC that the waves west of Lata had travelled some 500m inland, and that three villages had been damaged.
Many of the homes in the area were semi-permanent, he said, and were reported to have been flattened.
Police were travelling to the area, he said, and the priority was to ensure the local airport is functioning so aid and supplies can be flown in.
Another government spokesman, George Herming, said reports suggested that between 60 to 70 homes have been damaged in four villages on Santa Cruz Islands.
A restive "super volcano" west of Naples is raising nervousness in the local Italian population. The ground of the Campi Flegrei "burning fields", also known as the Phlegraean Fields, has risen more in recent weeks than it has in a long time.
Are we witnessing the start of a historic financial meltdown in Europe? In recent days, two massive corruption scandals have greatly shaken confidence in European financial markets. The first involves Spanish Prime Minister Mariano Rajoy. It is being alleged that he has been receiving illegal cash payments, and the calls for his resignation grow louder with each passing day. The second is a derivatives scandal at the third largest bank in Italy. Allegedly, there were some very large unreported derivatives deals that were supposed to help hide losses at the bank, but instead they actually made the losses much larger. The investigation that is looking into this derivatives scandal is starting to spread to other banks, and nobody is quite sure how far down the rabbit hole this thing goes. But what everyone does agree on is that this derivatives scandal has shaken up Italian politics, and the outcome of the upcoming election is now very uncertain. Former Prime Minister Silvio Berlusconi is rapidly rising in the polls, and the European establishment is less than thrilled about that. Meanwhile, stock indexes all over Europe fell rapidly on Monday, and even the Dow was down 129 points. So will all this blow over in a few days, or is this the beginning of a full-blown stock market crash in Europe?
That is a very good question. Perhaps there would not be so much concern if the overall European economy was doing well, but the truth is that the underlying economic fundamentals in Europe have continued to get even worse. The unemployment rate in the eurozone is at an all-time high, and the unemployment rates in both Greece and Spain are now over 26 percent. Much of southern Europe is already in the midst of a full-blown economic depression, so it really has been remarkable that the financial markets in Europe have been able to hold up as well as they have so far.
In fact, the entire globe is on the verge of a debt implosion. This was something that Bill Gross of Pimco discussed in his February newsletter…
“So our credit-based financial markets and the economy it supports are levered, fragile and increasingly entropic – it is running out of energy and time. When does money run out of time? The countdown begins when investable assets pose too much risk for too little return; when lenders desert credit markets for other alternatives such as cash or real assets.”
No debt bubble can expand indefinitely. At some point it can no longer hold itself together.
Europe is rapidly approaching that point, and so is the United States.
So how much time do we have left?
Iran already has nuclear capabilities but is not interested in attacking Israel, Iranian President Mahmoud Ahmadinejad said in an interview published Wednesday in the Egyptian media.
Ahmadinejad arrived in Egypt on Tuesday on the first trip by an Iranian head of state since the 1979 revolution, underlining the thaw in relations since Egyptians elected an Islamist head of state last year. The president's visit to Cairo is for an Islamic summit due to begin Wednesday.
The world must now relate to Iran as an atomic power, Ahmadinejad told Al-Ahram, as it is "already a nuclear state." He said that Tehran does not seek a military confrontation with Israel, and did not threaten to strike the "Zionist entity." In fact, Al-Ahram quoted him as saying, all of Iran's military capabilities are "defensive".