The first thing I would say about modal verbs is that their usage extends over many different contexts and so any general rules are bound to fail when taken out of context.
Outline
- Use of 'will' and 'would' to express belief
- Other uses
- The answer
1. Use of 'will' and 'would' to express belief
(Credit for this section should go to @snailboat)
To illustrate the difference in use of 'will' and 'would' for expressing certainty, snailboat suggested the following sentences at the ELL chat room:
1A. I'm sure they have been looking for those bank robbers.
1B. I'm sure they will have been looking for those bank robbers.
2A. I'm sure they had been looking for those bank robbers.
2B. I'm sure they would have been looking for those bank robbers.
In sentences 1A (they have been) and 2A (they had been) the speaker knows they have/had been looking for those bank robbers. The main difference is that the use of present perfect in 1A (they have been) indicates that the search has lasted at least until now.
In sentences 1B (they will have been) and 2B (they would have been) the speaker expresses a belief:
in sentence 1B (they will have been), the speaker expresses the belief that they have been looking for those bank robbers.
in sentence 2B (they would have been) the speaker expresses the belief that they had been looking for those bank robbers.
2. Other uses
Again, a word of caution, the interpretation above is not unique and can change if the context changes. This section shows other possible uses of will have been and would have been.
3. The answer
Let's now consider the example in your question:
A: We saw a police helicopter yesterday morning.
B: I'm sure they would have been looking for those bank robbers.
To be able to use "will have been" is necessary to change the context as described in the first section of this answer:
A: We have seen a police helicopter.
B: I'm sure they will have been looking for those bank robbers.
If learning to drive is a short-term event that spans a few weeks or months, there's nothing wrong with saying:
My father learned to drive when he was 16.
If you want to emphasize, however, that learning to drive is more than a one-time event, that it's a never-ending accumulation of experiences and ongoing lessons on the road, then you would say:
My father has been learning to drive since he was 16.
If you simply want to emphasize how long he's been driving, then use the simpler:
My father has been driving since he was 16.
All three sentences reveal that your father first got behind a steering wheel at the age of 16, but they focus on three different aspects of driving: learning the fundamentals of driving, becoming an expert at driving, and just plain driving.
Now, about these two:
It is 5 years since I last saw her.
It has been 5 years since I last saw her.
Don't fall into the trap of thinking that one of these must be correct, and therefore the other must be wrong. I see that so much on the pages of ELL!
Sometimes one alternative is correct while another is wrong, but oftentimes both answers are correct, and it's just a matter of context: Are you speaking, or writing? Are you in New York, or in Sydney? Is the environment formal, or informal? I say lotsa things among friends that I probably wouldn't write in a research paper, and I've inserted many phraseologies into research papers that I would be highly unlikely to utter around friends.
I don't find any grammatical gaffe in either of the "5 years" sentences you wrote here (other than, in writing, we would usually write the word five instead of the numeral 5; we do that for single-digit numbers). However, your teacher's wording sounds too formal and stilted for casual conversation – at least in my opinion and according to where I live – so I'd probably default to your wording about 90% of the time.
As for getting some of your English lessons by watching movies, that's a two-edged sword. I'd be careful about that. On one hand, movies can give you a good feel for how people speak English in everyday life. On the other hand, not everything you read in a movie script is worth emulating. Movie directors want actors to say things in accordance with the characters in their films. So, if you watch too many mafia movies, you might end up speaking like a mobster. I don't think my wife would appreciate me saying, "Yo, Annabelle" – no matter how much she may have liked the original Rocky movie.
Best Answer
There are two separate phrases in your question.
The first is: in what sense which, as you correctly surmise, is another way of saying in what way.
The second is: as in, a phrase that is generally used to introduce an example or category, which you illustrate correctly.
Most of the time, instead of saying as in, you might say referring to, signifying or meaning.
So you might say to someone, I am interested in the origins of the word sow as in (meaning, referring to) seeds rather than sew (referring to, signifying) as in clothes.