1. Interpretation of the question

To "remove all the mass of the earth to infinity" means to completely disperse the Earth so that every small mass element is taken from its position inside the Earth to infinity.

The required energy is the gravitational binding energy of a uniform spherical mass distribution.

2. Known result for gravitational self-energy of a solid sphere

For a uniform solid sphere of mass $M$ and radius $R$, the gravitational potential energy is

$U = -\frac{3GM^2}{5R}$

Therefore, the energy required to break it up completely and take all mass to infinity is the magnitude:

$E = \frac{3GM^2}{5R}$

3. Match with the given form

Given:

$E = \frac{x}{5}\frac{GM^2}{R}$

Comparing with

$E = \frac{3}{5}\frac{GM^2}{R}$

we get

$x = 3$

4. Final answer

$\boxed{3}$

5. Comparison with stored answer

Stored correct answer = $3$

This matches our derived answer.