Video solution:

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Written solution:

Let $x$ be the first term and $y$ be the second.

Then we get the following sequence. $$x, y, xy, xy^2, x^2y^3, x^3y^5, \cdots$$ From this, we get that $x^3y^5 = 4000.$

Factoring $4000,$ we get $$4000 = 2^5 \cdot 5^3.$$ We need $x$ and $y$ to be integers. The only fifth powers that divides $4000$ are $1$ and $32.$

If $y = 1,$ then $x^3 = 4000,$ which doesn't work since $4000$ is not a perfect cube. Therefore, $$y^5 = 32$$$$y = 2.$$

This forces $x$ to equal $5.$

Thus, D is the correct answer.