We denote by \(\mathcal {H}_{d,g,r}\) the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in \(\mathbb {P}^r\) . In this article, we study \(\mathcal {H}_{16,g,5}\) for almost every possible genus g and chasing after its irreducibility. We also study the natural moduli map \(\mathcal {H}_{d,g,5}{\mathop {\xrightarrow {\phantom{a} }}\limits ^{\mu }}\mathcal {M}_g\) and several key properties such as gonality of a general element as well as characterizing smooth elements in each component.
