The bank said the aim was to speed up the adoption of new technology and "continue to lead in digital banking".
It said 3,500 jobs would go in Belgium and 2,300 in the Netherlands. It expects to make savings of €900m (£780m; $1bn) a year.
ING said it was setting aside €1.1bn to pay for redundancies.
The bank currently employs 51,833 people.
ING chief executive Ralph Hamers said that all in all, over the coming five years, about 7,000 jobs might be "impacted", including 950 positions employed by external suppliers.
"Customers are increasingly digital and bank with us more and more through mobile devices," said Mr Hamers.
"Their needs and expectations are the same, all over the world, and they expect us to adopt new technology as fast as companies in other sectors.
"In order to continue to lead in digital banking, we need to offer a better customer experience, that's instant, personal, frictionless and relevant."
He added: "From 2016 to 2021, we intend to invest €800m in our digital transformation, building a scalable platform to cater for continued commercial growth, an improved customer experience and a quicker delivery of new products."
Last week, Germany's second-biggest lender, Commerzbank, said it was planning to cut 9,600 jobs over the next four years and end dividend payments for the first time.
Big banks in general are facing challenges from new competition and the higher cost of new regulations, while at the same time, ultra-low interest rates are hitting profits.
Dutch bank ING says it intends to cut about 5,800 jobs in Belgium and the Netherlands over the next five years as part of a cost-cutting plan.