In reality the captain would hard fail - he's not going to understand the locals for one. Also there was a reason that the industrial revolution came about when it did. It needed a hell of a lot of very different cultural, societial, scientific and technological things to be 'in place'. One man is not going to change the world that much.

However, I'd guess that the captain has help from technology of his time to get over the various humps and barriers for the story to work.

If it was me that was thrown back to the fifth century, sure I would know a lot, but actually trying to get anything you knew to actually succeed would be almost impossible! For example, I know very basically how you make steel. But to actually make a furnace that reliably makes steel would, I imagine, really be a lifelong project with a lot of trial and error with the basic tech of the time.

To give an interesting example, mathematics is at the core of modern technology (and I assume his!), yet the mathematicians of the 5th century would just not understand your use of numbers. To them geometry was the core of all maths, and if you couldn't represent a problem without a geometric representation it just wasn't correct, negative numbers were meaningless to them. There was no algebra, no equations in the sense that we easily see them, no zero and don't get me started on how difficult it would be to convinced that imaginary numbers are real and useful! The only 'real' numbers were natural numbers. Even fractions were not deemed to be the same sort of object as a 'real number'. It would probably take another lifetime to convince thinkers of the age that even your basic understanding of mathematics (so not getting into really interesting stuff like differential calculus) was correct or useful