Exercise 111.60.3. Let $k$ be an algebraically closed field. Consider the closed subset $X$ of $k^5$ with Zariski topology and coordinates $x_1, x_2, x_3, x_4, x_5$ given by the equations

\[ x_1^2 - x_4 = 0,\quad x_2^5 - x_5 = 0,\quad x_3^2 + x_3 + x_4 + x_5 = 0 \]

What is the dimension of $X$ and why?

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