If a country has 5% real GDP growth and 5% population growth, what is the growth rate of real GDP per capita?

0%

Explanation:

It is easier to explain using an example:

the country's real GDP during year 1 = $1,000,000

the country's population during year 1 = 1,000 people

the real GDP per capita = $1,000,000 / 1,000 people = $1,000 per person

during year 2, both the real GDP and the population grow by 5%

the country's real GDP during year 2 = $1,050,000

the country's population during year 2 = 1,050 people

the real GDP per capita = $1,050,000 / 1,050 people = $1,000 per person

so there has been no change in the real GDP per capita.