Suppose \(f:R\to (0,\infty )\) be a differentiable function such that \(5f(x+y)=f(x).f(y),\forall x,y\in \mathrm{R}\). I…

Suppose \(f:R\to (0,\infty )\) be a differentiable function such that \(5f(x+y)=f(x).f(y),\forall x,y\in \mathrm{R}\). If \(f(3)=320\), then \(\sum _{n=0}^{5}f(n)\) is equal to:

[JEE Main 2023, 30 Jan (Shift 1)]