Sigmafy the expression

Mathematica, 17 14 13 bytes

Thanks to Ian Miller for saving 3 bytes.

Thanks to LegionMammal978 for saving 1 byte.

#~NSum~{k,5}&

The input should be an actual expression containing k, e.g.:

#~NSum~{k,5}&[Sqrt[k]^3+4]

Python 3, 40 37 bytes

3 bytes thanks to Arnauld.

Eval scope tricks \o/

f=lambda s,k=5:k and eval(s)+f(s,k-1)

Try it online!

Uses k**0.5 instead of sqrt(k).

JavaScript (ES7), 31 30 bytes

Uses k**0.5 for sqrt(k).

f=(e,k=6)=>--k&&f(e,k)+eval(e)

console.log(f("2*k"))
console.log(f("k**0.5"))
console.log(f("k+k/2+k**2"))
console.log(f("k**2"))

Try it online!