What does $o(x^4)$ mean in the following series expansion?

Question

Given $$f(x)=\sin^2(x)-x^2e^{-x}$$ I know the series expansion for $\sin(x)$ and $e^{-x}$ and so I wrote: $$f(x)=(x-x^3/3!+x^5/5!-....)^2-x^2(1-x+x^2/2!-x^3/3!+....)$$ I am finding it difficult to proceed beyond this point as I'm having trouble in squarign the series $\sin(x)$. However the author, further writes $$f(x)=x^2-x^4/3+o(x^5)-x^2+x^3-x^4/2+o(x^4)=x^3-5x^4/6+o(x^4)$$ What does $o(x^5)$ and $o(x^4)$ mean and what rules should one follow in order to determmine the power of $x$ that goes in the expression $o(x^n)$?