Soffit or gutter repair?
 

I would appreciate your advice and recommendations on the attached photo of a soffit from the front of our home, where you should see that rust is forming. (I also just noticed that the gutters need to be cleaned—and that has been scheduled.). Regarding the soffit, what would cause this, and what type of vendor would you use to repair this?

Many thanks in advance.

Note: this is my first attempt at trying to include a photo!

Gutters are typically made from aluminum, no rust, I think you are seeing mold. Rust is typically a brown color, the photos appear to have black, aka mold. Without being able to see the top of the gutter, I would:
1. Power wash the area.
2. As noted have the gutters cleaned and then make sure they drain correctly.
3. See if the end cap on the gutter is properly sealed to the gutter.
IMHO, this looks like the end cap is leaking and the result is mold in the area.
Hope this helps.

Thank you!