My goal is over 750.

My goal was a score over 750 [Alternative: My goal was to score over 750]

Titles are not usually complete sentences in English, and they don't end in a period.

My goal was to score over 750 points.

I usually practiced/studied for about 5 hours a day.

"Homework" is usually work assigned by a teacher for a student to do at home, not work that one chooses to do oneself.

And I did it about 15 hours a day during the week-long vacation in May called "Golden Week" in Japan.

And the result was...

I didn't achieve my goal (this time).

I'm not good at the reading part.

I need to study more grammar to get over 750 points.

I realized that my ability isn't good/strong enough yet. [More natural alternatives: I realized that I don't know enough yet. I realized that I need more work on my skills.]

I'm going to take the next TOEIC exam just one month from now.

The word "later" is not used when the point of reference is "now".

I'd like to reach my goal next time.

My goal is to score over 750.

this sentence needed clarity

And I did it my homework about 15 hours a day on during a week vacation of in May called Golden Week in Japan.

I got scored 730 points on it.

I couldn't didn't reach my aim.

I'm not good at the reading part.

I realize that My abilitty my skills isn't good enough yet.

I'm going to take next TOEIC exam just one month later next month.

My goal was to achieve over 750 points.