Is there any way to see other alien moves to check if it is others fighting that causes this trouble?
I'm pretty sure this is not possible. But it is very likely to be the cause of the issue, it can often be the case that a big war between aliens somewhere completely different in the galaxy can cause this for some time. How likely this is to happen depends greatly on how the game is setup, how many NPRs, chance of them generating, and so on.
Or possibly to manually override the 5 sec slowdown?
This isn't possible. Steve has mentioned in the past that the reason for this is because the only way to do it would be to make the game not work the way it's supposed to. I.e, the detailed combat and options surrounding it mean that if there is a big combat somewhere, the game has to slow down to handle it. It's sort of one of those things where, to have one you have to accept the other. Opinions may vary of course on the wisdom of having all of that complexity in the game, but it is what it is.