Identify the compound

Copper(II) sulfate pentahydrate is written as: $\mathrm{CuSO_4\cdot 5H_2O}$

Understand “directly bonded to the centre”

Here, the “centre” is the metal ion $\mathrm{Cu^{2+}}$.

In hydrated copper(II) sulfate, the actual structure is: $\mathrm{[Cu(H_2O)_4]SO_4\cdot H_2O}$

Count the coordinated water molecules

In $\mathrm{[Cu(H_2O)_4]^{2+}}$ the number of water molecules directly bonded (coordinated) to $\mathrm{Cu^{2+}}$ is: $4$

What about the 5th water molecule?

The fifth water molecule is not directly bonded to copper. It is present as water of crystallization.

Final answer

Therefore, the number of water molecules directly bonded to the central metal ion in $\mathrm{CuSO_4\cdot 5H_2O}$ is: $\boxed{4}$