Step 1: Recall the reaction of alcohols with PCl$_5$.
Phosphorus pentachloride (PCl$_5$) reacts with alcohols to replace the hydroxyl (-OH) group with a chlorine atom (-Cl), forming an alkyl chloride. The other products of this reaction are phosphorus oxychloride (POCl$_3$) and hydrogen chloride (HCl).
Step 2: Apply the reaction to ethanol.
Ethanol has the formula CH$_3$CH$_2$OH. When it reacts with PCl$_5$, the -OH group is replaced by -Cl, forming chloroethane (CH$_3$CH$_2$Cl). The other products will be POCl$_3$ and HCl.
The balanced chemical equation for the reaction is:
$$ \text{CH}_3\text{CH}_2\text{OH} + \text{PCl}_5 \rightarrow \text{CH}_3\text{CH}_2\text{Cl} + \text{POCl}_3 + \text{HCl} $$
Ethanol + Phosphorus pentachloride $\rightarrow$ Chloroethane + Phosphorous oxychloride + Hydrochloric acid
Step 3: Identify the correct products from the options.
Option (4) lists Chloroethane, Hydrochloric acid, and Phosphorous oxy chloride as the products, which matches the expected products of the reaction.
Final Answer:
\[
\boxed{\text{Chloroethane, Hydrochloric acid and Phosphorous oxy chloride}}
\]