Step 1: Understanding the compound.
CuSO\(_4\cdot 5H_2O\) is known as copper(II) sulfate pentahydrate. It contains 5 water molecules per formula unit.
Step 2: Coordination concept.
Out of the 5 water molecules, 4 are directly bonded (coordinated) to the copper(II) ion forming the complex [Cu(H\(_2\)O)\(_4\)]\(^{2+}\).
Step 3: Hydrogen bonding.
The remaining 1 water molecule is not directly bonded to Cu\(^{2+}\) and exists as a lattice water molecule, hydrogen bonded in the crystal structure.
Step 4: Conclusion.
Hence, the number of coordinated and hydrogen bonded water molecules are 4 and 1, respectively.