Thank you for your help.

3. He goes to the academy to take three subjects.
4. He goes to the specific academy to take three subjects. [specific]
5. He goes to the academy in general to take three subjects. [in generic use]
[What about #3? Does #3 mean #4 or #5?]

3 - OK

4 - I wouldn't use the word "specific" like this. I'd write this sentence like this:
He goes to the Adamston Academy to take French, guitar, and advanced math courses.

5 - I would not write this sentence this way; it's quite awkward. I'd write this:
He goes to an academy to take French, guitar, and advanced math courses.

I appreciate your help.

3. He goes to the academy to take three subjects.

[What about 'the academy' in #3? Does 'the acdemy' in generic use? Or does 'the academy' mean the academy which the speaker and hearer know already?]

Yes, your second version of #3 is fine.

To understand the distinction between sentences 3, 4, and 5, let's break them down and analyze their meanings:

3. "He goes to the academy to take three subjects."

In this sentence, it implies that the person is going to an unspecified or unspecified academy to study three particular subjects. It doesn't specify whether it's a specific or general academy, so we can't infer that it means #4 or #5 specifically.

4. "He goes to the specific academy to take three subjects."

Sentence 4 explicitly mentions that the person is going to a specific academy, suggesting that there is a particular academy they are attending to study three subjects. It assumes that there is a specific academy being referred to.

5. "He goes to the academy in general to take three subjects."

Sentence 5 suggests that the person is going to an academy in general, meaning any academy, to study three subjects. It conveys a more generic meaning of attending any academy to pursue these subjects.

So, based on these explanations:

- Sentence 3 does not explicitly indicate whether it means #4 or #5.
- Sentence 4 implies attending a specific academy to study three subjects.
- Sentence 5 implies attending any academy to study three subjects.

Without further context or clarification, sentence 3 could apply to either #4 or #5.