Is my £1000 Personal Savings Allowance included in my Starting Savings Rate of £5000?

My only income is my basic state pension of £10770. Please can you tell me if I can earn up to £6000 in savings interest without paying tax on it (via my Personal Savings Allowance of £1000 and my Starting Savings Rate of £5000). Or is the PSA £1000 included in the Starting Rate for Savings? Many thanks.

Hi J Thoms,
You have both.
Thank you. 
 

Many thanks. I was advised by the tax office to work on the basis that the £5000 Starting rate for Savings included the £1000 Personal Savings Allowance as they weren't sure. I appreciate the clarification. Kind regards.