7. Let $P(x)=x^{5}-x^{2}+1$ have five roots $r_{1}$,
$$
\begin{array}{l}
r_{2}, \cdots, r_{5}, Q(x)=x^{2}+1 \text {. Then } \\
\quad Q\left(r_{1}\right) Q\left(r_{2}\right) Q\left(r_{3}\right) Q\left(r_{4}\right) Q\left(r_{5}\right) \\
\quad=
\end{array}
$$
7. 5.

From the problem, we know $P(x)=\prod_{j=1}^{5}\left(x-r_{j}\right)$.
$$
\begin{array}{l}
\text { Then } \prod_{j=1}^{5} Q\left(r_{j}\right)=\left(\prod_{j=1}^{5}\left(r_{j}+\mathrm{i}\right)\right)\left(\prod_{j=1}^{5}\left(r_{j}-\mathrm{i}\right)\right) \\
=P(\mathrm{i}) P(-\mathrm{i}) \\
=\left(\mathrm{i}^{5}-\mathrm{i}^{2}+1\right)\left((-\mathrm{i})^{5}-(-\mathrm{i})^{2}+1\right) \\
=(\mathrm{i}+2)(-\mathrm{i}+2)=5 .
\end{array}
$$