Maximum-Score-224's journey

I was informed that my last day at my job would be July 10 due to a layoff. I've started interviewing for new positions, and I'm wondering about my availability. If a recruiter asks when I can start, is it acceptable to say July 13? I’m a bit concerned about how to explain my situation if they ask why I’m available so soon. Should I mention that I was laid off, or would that create a negative impression? I’ve received advice suggesting that it’s fine to be honest but to keep my explanation straightforward during interviews.