Alex Salmond spoke out as a new paper was published by the Scottish Government, detailing how it believes a Yes vote in September's referendum could help boost the economy north of the border.
An increase of 0.3 percentage points in the long run productivity growth rate could raise an additional £2.4 billion a year in revenues by 2029/30, according to the Scottish Government.
Meanwhile, upping the employment rate in Scotland by 3.3 percentage points - taking it to the level of the five best-performing countries in the developed world - could provide additional revenues of £1.3 billion a year, the paper claims.
A rise in the population, which is less than the UK as a whole is expected to see, could net a further £1.5 billion a year by 2029/30, it argues.
Mr Salmond said the Outlook For Scotland's Public Finances paper "gives a very clear picture of what independence could deliver in economic terms for the people of Scotland".
He argued: "By increasing productivity by 0.3 percentage points per annum, boosting the working-age population by less than the predicted UK rate, and increasing the employment rate by just over three percentage points, bringing Scotland up to the same standard as the top countries in the OECD, we can generate over £5 billion a year of extra revenues within 15 years, without increasing tax by a penny.
"Scotland is one of the wealthiest countries in the world, more prosperous per head than the UK, France and Japan, but we need the powers of independence to ensure that that wealth properly benefits everyone in our society.
"That wealth means we will start life as an independent nation with strong finances and huge economic potential.
"The latest figures show that by using the powers that only independence will bring we can deliver an independence bonus with increased revenues for Scotland.
"The choice Scotland will make in September is between the opportunity to grow our economy, to boost revenues and to invest in public services, or to continue with an economic policy set in Westminster that ignores Scotland's needs.
"This analysis shows that on all headline measures of the public finances, Scotland's fiscal position is forecast to be stronger than, or at the very least level with, the UK position."
The total "bonus" is worth about £1,000 for every person in Scotland, Mr Salmond said.
"We project that over a 15-year period, the tax revenue addition is £5 billion - around £1,000 a head for every man, woman and child in Scotland, or some £2,000 for each Scottish family," he said.
"We describe that as the bonus of independence - the independence bonus.
"Not caused by increase in taxes, but by increase in productivity, increase in the working-age population and an increase in employment.
"These figures encapsulate the difference between the two campaigns that will be played out over the next three months and more.
"Our campaign is being based on putting forward the potential of the Scottish economy, understanding the strengths this country has."
The anti-independence campaign is based on fear, he claimed.
"We don't think that scaremongering stands up to a moment's examination," Mr Salmond said.
The financial details are published six months after the Scottish Government's heavily-anticipated White Paper on independence.
At the same time, an updated oil and gas report sets out projections for North Sea tax receipts.
The Scottish Government's intervention comes on the same day the Treasury publishes its own work which claims to reveal the cost of independence.
But the UK Government's figure of £2.7 billion is heavily disputed - not least by the academic whose research underpinned the prediction.
Professor Patrick Dunleavy, of the London School of Economics, told the Financial Times that the Treasury's figures are "bizarrely inaccurate".
"I don't see why the Scottish Government couldn't do this for a very small amount of money," he said.
Mr Salmond, speaking at Scottish Government headquarters in Edinburgh, said the figures have been badly manipulated and were more likely to be in the region of £250 million.
He said further research by Professor Robert Young of the University of Western Ontario, which puts the figure at £1.5 billion, had also been misrepresented.
The First Minister said: "This is the most devastating hole blown in the Treasury's assumptions - not just assumptions about administrative costs, the set-up costs of an independent Scotland, but also it typifies their entire approach to this debate.
"It is a blow to Treasury credibility and the credibility of the UK Government and 'project fear' and the Better Together campaign from which they'll find it extremely difficult to recover."
But the First Minister said no detailed work has been done by the Scottish Government to work out its own total figure for the cost of independence.
Instead, he said any set-up cost has to take into account the £110 billion share of UK assets Scotland could be entitled to in negotiations after independence.
Evidence of savings are already seen in the creation of the new tax body Revenue Scotland, he argued.
Buying services from HM Revenue and Customs would have cost £22.3 million over seven years while the "actual" cost of using Revenue Scotland will be £16.7 million, he said.
"We think that's a reasonable estimate that Prof Dunleavy, an expert in the field, has made and we put it into the context of a share of the assets that is worth £110 billion - that's 400 times the potential start-up costs of what share Scotland would be entitled to," he said.