**Solution:**

To find the work done in moving a charge q from the centre of the first ring to the centre of the second ring, we can break it down into two steps:

1. Calculating the electric potential at the center of the first ring.
2. Calculating the work done in moving the charge q from the first ring to the second ring.

**Step 1: Calculating the Electric Potential at the Center of the First Ring**

The electric potential at the center of a uniformly charged ring can be calculated using the formula:

V = k * Q / r

Where:
- V is the electric potential
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- Q is the charge on the ring
- r is the radius of the ring

For the first ring, Q = 10 C and r = 10 cm = 0.1 m, so the electric potential at the center of the first ring is:

V1 = (9 x 10^9 Nm^2/C^2) * (10 C) / (0.1 m) = 9 x 10^11 V

**Step 2: Calculating the Work Done in Moving the Charge q**

The work done in moving a charge q from one point to another can be calculated using the formula:

W = q * (V2 - V1)

Where:
- W is the work done
- q is the charge being moved
- V2 is the final electric potential
- V1 is the initial electric potential

In this case, q is the charge being moved from the center of the first ring to the center of the second ring. The electric potential at the center of the second ring can be calculated using the same formula as in step 1, with Q = 5 C and r = 10 cm = 0.1 m:

V2 = (9 x 10^9 Nm^2/C^2) * (5 C) / (0.1 m) = 4.5 x 10^11 V

Substituting the values into the work formula:

W = q * (V2 - V1)
W = q * (4.5 x 10^11 V - 9 x 10^11 V)
W = q * (-4.5 x 10^11 V)

So the work done in moving the charge q from the center of the first ring to the center of the second ring is -4.5 x 10^11 times the charge q. The negative sign indicates that work is done against the electric field, meaning external work is required to move the charge q.