A pH of 5 to 6.5 looks a bit large of a range to me. Most manufacturers of nutes show a range of 1 but typically we use a range of around half that.
Peat is a problem medium because of its low pH and this is often offset with a lime buffer to raise it, but the lime will be ansorbed by the plant and washed out the bottom of the pot, then what? I guess add more lime