Answer
$-26.12\;\rm rad/s^2$
Work Step by Step
First of all, we need o convert the angular velocities in the given table from rpm to rad per second.
To do that we need to multiply by $\rm\dfrac{(2\pi\;\rm rad)\cdot
( 1\; min) }{(1\; rev)\cdot(60\;s)}=\dfrac{2\pi}{60}$
Thus,
\begin{array}{|c|c|c|}
\hline
{\rm Time\;(s)} & \omega\;{\rm (rad/s)} \\
\hline
0 & 315.21 \\
\hline
1 & 294.26\\
\hline
2 & 256.56\\
\hline
3 & 235.62\\
\hline
4 & 203.16 \\
\hline
5 & 189.54 \\
\hline
6 & 158.13 \\
\hline
\end{array}
Now we can plug these dots and draw the best get line, as you see in the figure below. Then we can find its slope.
And as we see the software calculator gave us a slope of -26.18 rad/s$^2$
Therefore,
$$\alpha=\color{red}{\bf -26.12}\;\rm rad/s^2$$