A long solenoid is constructed by tightly winding a wire of radius...

The magnetic field at the centre of a long solenoid is given by $B = \mu_0 n I$, where $n$ is the number of turns per unit length.

Since the wire is tightly wound, the distance between successive turns is equal to the diameter of the wire.

Diameter of the wire $d = 2r = 2 \times 0.5 \text{ mm} = 1 \text{ mm} = 10^{-3} \text{ m}$.

The number of turns per unit length is $n = \dfrac{1}{d} = \dfrac{1}{10^{-3}} = 1000 \text{ m}^{-1}$.

Substituting the values in the formula for magnetic field:

$B = 4\pi \times 10^{-7} \times 1000 \times 5$

$B = 20\pi \times 10^{-4} \text{ T} = 2\pi \times 10^{-3} \text{ T}$.