Is this correct way of replying with available dates for an interview

I think it would be better to mention it as your convenience rather than availability. Here is an example:

It would be convenient for me to have the interview on 5th, 10th or 18th of August. Do please check your calendar and inform me when it could be scheduled.

Here you may mention the dates in any form respective to the proximity.

Replying to a solicitation for a job interview should be done in the context of making such an interview convenient for the prospective employer, not the employee. Further, any reply that narrowed opportunities to only a handful of dates can create the notion that interviewing for this prospective job is something you'll do if nothing better or more important appears on your schedule. On that basis, I would respectfully disagree with the selected answer and submit the following:

"I will make every effort to accommodate your earliest convenience for an interview. My schedule shows that I have no conflicts on August 16th, 18th, and 19th."

The objective is two-fold: Be gracious and deferential to the prospective employer, and provide specific dates for which scheduling would be simplest.