The gravitational force between two objects due to their masses is
#F=G(m_1m_2)/r^2#
where
#F=#force in newtons
#m_1=#mass of first object in kilograms
#m_2=#mass of second object in kilograms
#r=#distance between centres of the objects in metres
#G=#the "gravitational constant", approximately equal to #6.674xx10^(-11)Nkg^(-2)m^2#
This idea was first formulated by Isaac Newton, and published by him in 1686.
So the gravitational force "goes as the inverse of #r^2#", which is to say that if you travel twice as far away, it will drop in size by factor #2^2=4#.
To drop the force by a factor 5, we must make the distance from the centre of the earth #sqrt(5)~=2.24# times what the distance is to the surface, i.e. a height of #(sqrt(5)-1)R# above the surface. Using the supplied value for #R#, this is to three significant figures a height of #7.87xx10^6# m#=7870# km. Note that this is outside earth's atmosphere (up to 100 km) and beyond "Low Earth Orbit" (up to 2000 km); it is within "Medium Earth Orbit". See https://en.wikipedia.org/wiki/Medium_Earth_orbit
To drop the force to zero, the distance has to become infinite - the graph of #1/r^2# becomes arbitrarily small as #r# becomes arbitrarily large, but it does not go to zero. Wherever you are in the universe, you will experience some contribution of earth's gravity - but in most places it will be such a tiny effect as to be undetectable, swamped by more local gravitational fields. So the force never becomes zero, although for practical purposes it becomes negligible when you move out far enough from earth that the much larger Sun's gravitational field makes it small in comparison.
