It stood at 4.74 million back in April 2016.
New Central Statistics Office (CSO) projections say the rise of just under two million people is expected, if there is high net inward migration and high fertility.
But even in a scenario with low migration and declining fertility, the population is still expected to reach 5.58 million in 2051.
The Population and Labour Force Projections 2017-2051 report also says the number of primary school-aged children will increase from its 2016 level of 548,100 to between 555,500 and 562,000 by 2021.
After that, the number of primary school pupils is expected to fall to between 510,900 and 457,600 by 2031.
While the secondary school-aged population will increase by between 67,300 and 75,700 people by 2026.
And by 2051, there will be between 330,300 and 439,600 secondary school-aged children.
The CSO also reveals that there will be between 1.5 and 1.6 million persons aged 65 years and over by 2051.
That is compared with 629,800 in 2016.
It says while some 13.3% of the population was aged 65 years and older in 2016, this will rise to between 23.9% and 27.4% in 2051.
The number of persons aged 80 years and over is set to grow from 147,800 in 2016 to up to 549,000 in 2051.
On the labour force, the CSO says: “Assuming net inward migration of 10,000 people annually… the labour force is expected to grow from 2,338,600 persons in 2016 to 2,628,700 in 2031”.
That is a rise of 12.4% over the period.
In a more optimistic scenario, there is a rise of 397,800 to a labour force of 2,736,400 persons in 2031 – while the most optimistic scenario has a rise of just over 500,000 people to 2,842,900.
Statistician James Hegarty says: “The report is not an attempt to predict the future but rather presents how the population could evolve under different scenarios.
“By making assumptions about future trends in mortality, migration and fertility, we can project the population forward and examine the possible outcomes for demographic groups such as the school-going population, the working-age population and the elderly.”