Advantages of FF$5$ over Fama$-$French $3-$Factor Model:

The Fama$-$French five$-$factor model extends the original three$-$factor model by including two additional factors: profitability and investment. The advantages of the FF$5$ model over the $3-$factor model include:

Explanation:

Better Capture of Anomalies: The FF$5$ model captures more of the anomalies observed in asset pricing. By introducing profitability and investment factors, it accounts for variations in returns that the $3-$factor model cannot explain adequately.

Improved Asset Pricing: The FF$5$ model offers a more comprehensive explanation of asset returns, making it a more robust tool for pricing assets. It can better differentiate between high and low returns, providing more precise estimates of expected returns.

Enhanced Portfolio Construction: The additional factors allow investors to create more diversified portfolios, as they consider not only market risk and size and value factors but also profitability and investment factors.