You're doing it pretty well by eye, but what if you wanted to have it at exactly the same angle?
From the next lesson, it sounds like you could do some math to calculate the angle based on the meter ticks, then type in angles, but is there a more elegant way to do this? Such as by having the pentagon created on that fuselage wall plane from the beginning?
Its certainly possible, but it's a bit tricky without the use of add-ons. I'd recommend checking out this quick tutorial by Aidy Burrows. He goes over the process of aligning two faces both manually and with the use of some Blender add-ons.
What I did was to open the snapping menu at the top, clicked on "Face", ticked "Align rotation to target", and also turned on snapping. Then I just moved the window to the face where I wanted it to be placed. The window did face the wrong side out, so I just rotated it 180 degrees on the X-axis.
I made the initial window pentagon/circle as a separate object and added a Shrinkwrap modifier to the window object with the rocket fuselage as the target. After applying the Shrinkwrap modifier, I could easily extrude from the window pentagon along the local axes.