Step 1: Identify element X from atomic number 13.
Atomic number 13 is Aluminium (Al), with electron configuration $1s^2 2s^2 2p^6 3s^2 3p^1$.
Step 2: Write the complex and list all ligands.
Complex: $[AlCl(H_2O)_5]^{2+}$. Ligands attached to Al: one $Cl^-$ and five $H_2O$ molecules.
Step 3: Determine the covalency of Al.
Covalency = total coordinate bonds formed by Al with ligands = $1 + 5 = 6$.
Step 4: Determine the oxidation state of Al.
Let oxidation state = $x$. Charges: $Cl^-$ gives $-1$; $H_2O$ gives 0; overall charge = $+2$. \[ x + (-1) + 5(0) = +2 \Rightarrow x = +3 \]
Step 5: Verify by cross-checking.
Al normally shows $+3$ oxidation state. Net charge: $(+3) + (-1) = +2$, consistent with $[AlCl(H_2O)_5]^{2+}$.
Step 6: State the final answer.
\[ \boxed{\text{Covalency} = 6,\ \text{Oxidation state} = +3} \]