Introduction:
In this problem, we are given that a satellite revolves around the earth in a circular orbit of radius 3R. We need to find the percentage increase in energy required to lift the satellite to an orbit of radius 5R.

Analysis:
To solve this problem, we need to understand the relationship between the radius of an orbit and the energy required to maintain the satellite in that orbit. The energy required to maintain a circular orbit is given by the formula:

E = -G * m * M / (2 * r)

Where:
- E is the energy required to maintain the orbit
- G is the gravitational constant
- m is the mass of the satellite
- M is the mass of the earth
- r is the radius of the orbit

Calculating the initial energy:
Given that the satellite is in a circular orbit of radius 3R, we can calculate the initial energy required to maintain this orbit. Let's denote this energy as E1.

E1 = -G * m * M / (2 * 3R)

Calculating the final energy:
Now, we need to calculate the energy required to lift the satellite to an orbit of radius 5R. Let's denote this energy as E2.

E2 = -G * m * M / (2 * 5R)

Calculating the percentage increase:
To find the percentage increase in energy, we can use the following formula:

Percentage Increase = (E2 - E1) / E1 * 100

Substituting the values of E1 and E2, we have:

Percentage Increase = (-G * m * M / (2 * 5R) - (-G * m * M / (2 * 3R))) / (-G * m * M / (2 * 3R)) * 100

Simplifying the expression:

Percentage Increase = (3R - 5R) / 5R * 100 = -2 / 5 * 100 = -40%

Conclusion:
The percentage increase in energy required to lift the satellite to an orbit of radius 5R is -40%. This means that the energy required to lift the satellite to a higher orbit is 40% less than the energy required to maintain it in the initial orbit.