The dead included four civilians, local military officials in Trincomalee, 260km northeast of Colombo, said on Monday.
The fifth person killed was a sailor on foot patrol.
Four other sailors and four civilians were wounded in the attack, carried out using a a mine rigged up to a bicycle, the military said.
They blamed Tamil Tiger separatists for carrying out the bombing.
"Two sailors approached the bicycle and were about to check it when the bomb went off," an official said.
"The civilians were travelling in the area in a three-wheel taxi at the time."
The attack came as Sri Lanka marked international labour day in low key fashion with all major political parties calling off their annual rallies fearing bomb attacks by the Liberation Tigers of Tamil Eelam (LTTE).
The government said all parties agreed to avoid large meetings after a female bomber killed herself and 10 others inside army headquarters in Colombo last Tuesday.
Rebels say civilians were killed in
government attacks last week
The military carried out air strikes against suspected Tiger positions in Trincomalee last week after the attack.
The rebels said at least 15 civilians died in the government strikes.
"We felt that if there were large crowds gathering at public places, they could be targets for bomb attacks," said Keheliya Rambukwella, the government spokesman on defence matters.
Some of the decorations and platforms set up for Monday's celebrations in Colombo were dismantled over the weekend.
In 1993 the then-president Ranasinghe Premadasa was assassinated by a suicide bomber at a May Day rally.
Tamil Tiger separatists, whom the authorities suspect of carrying out the recent Colombo attack, are leading a drawn-out campaign for independence for minority Tamils in the island's northeast.
More than 60,000 people have died in the separatist conflict since 1972.
More than 60,000 people have
died in the conflict since 1972
Monday's blast in Trincomalee was the latest in a worsening series of incidents to shake a four-year-old ceasefire between the government and the Tigers.
Nearly 200 people have been killed in the past month alone, according to figures given by the two sides.
In a separate attack on Monday, another five sailors were wounded when seaborne Tigers fired on a naval gunboat in waters off Trincomalee, military officials said.
"At least two big boats of the LTTE were involved and a (navy) Dvora gunboat was able to repulse the attack," an official in Trincomalee said.
A pro-separatist website said on Monday that the Tigers had moved an unspecified number of fighters along the island's northeastern coast to Trincomalee, in defiance of the ceasefire's ban on sea transport.
Tamilnet.com said the rebel boats came under attack from shore-based artillery, which the Sea Tigers countered.
The town of Trincomalee has been under night curfew since a massive bomb exploded at the local market on April 12, killing 17 people, mostly civilians.
The government and many Sinhalese locals blame the Tigers for the blast.
Faced with the recent escalation of violence, peace broker Norway has been trying to arrange a fresh round of talks amid mounting international pressure on both sides to return to the table.