Give an example of a vector space which has 125 elements

Question

Give an example of a vector space which has 125 elements. I don't know how proceed!!! Is there any technique about the field??

Answer 1

Just consider the field $\mathbb Z_5$ and mutiply it $3$ times with itself. Then new set over the field $\mathbb Z_5$ is a vector space with $125$ elements.

Answer 2

$\frac{\mathbb{Z}_5[x]}{(x^3)}$ as a $\mathbb{Z}_5$-module, which is $\{a+bx+cx^2\mid a,b,c\in\mathbb{Z}_5\}$.

This is the same as $$V=\left < [a,b,c]\mid a,b,c\in\mathbb{Z}_5\right>$$

which have $5^3=125$ elements.