Step 1: Identify the element \(X\).
The atomic number of the element is
\[
13
\]
Atomic number \(13\) corresponds to aluminium (\(Al\)).
Step 2: Determine the covalency of the central metal atom.
The complex is
\[
[XCl(H_2O)_5]^{2+}
\]
Here, the ligands attached to the metal are:
\[
1\,Cl^- \quad \text{and} \quad 5\,H_2O
\]
Thus, total number of coordinate bonds formed by the metal is
\[
1+5=6
\]
Therefore, the covalency of the metal is
\[
6
\]
Step 3: Determine the oxidation state of \(X\).
Let the oxidation state of \(X\) be \(x\).
The charge on the complex ion is
\[
+2
\]
The charge on ligands:
\[
Cl^-=-1
\]
\[
H_2O=0
\]
Applying charge balance,
\[
x+(-1)+5(0)=+2
\]
\[
x-1=2
\]
\[
x=+3
\]
Step 4: Final conclusion.
Therefore, the covalency and oxidation state of \(X\) are
\[
\boxed{6,\,+3}
\]