Answer
No.
Work Step by Step
To test if $x=\frac{3}{5}$ is a zero, evaluate $f(\frac{3}{5})=2(\frac{3}{5})^6-5(\frac{3}{5})^4+(\frac{3}{5})^3-(\frac{3}{5})+1\approx0.06$ and this is the remainder. As the remainder is not zero, $x=\frac{3}{5}$ is not a zero of the function.