1. ‘To be able to’ is used to express ability in all tenses and it also substitutes ‘can’ in all the forms in which it is not possible. Examples:
We weren’t able to open the door
She has never been able to learn German
He had never been able to solve the problem
Next month I will be able to drive a car

2. ‘Could’ or ‘be able to’ ? I could speak Spanish so I was able to understand and answer all his questions
Could to talk about habitual or permanent abilities in the past
Be able to to talk about abilities in a specific moment of the past
Ex: when I was a child I could ski.
Ex: I was able to open the door in the end

3. Note well Could is always possible in the negative form, even when we are talking about a specific moment in the past. Ex:
I was so tired that I couldn’t reach the top of the mountain. =
I was so tired that I wasn’t able to reach the top of the mountain

4. Some more examples Jack was an excellent tennis player.
He could beat anybody. (he had the general ability to beat anybody)

5. Some more examples
Jack and Alf had a game yesterday. Alf played very well but in the end Jack managed/ was able to beat him.

6. Some more examples
The fire spread through the building quickly , the small boy could leave the building but he didn’t because he wanted to rescue the cat.
The fire spread through the building quickly ,but everybody was able to /managed to escape (they were successful in leaving the building)