That looks good to me! The first monostable should hold off the second one by about 5.2 seconds and the output pulse should be about 1 second.
The resistor marked "33" should be "33K".
As a precaution against noise or supply instability, it would be a good idea to add a capacitor of about 100nF directly across the supply pins of the 555s, they are not essential but it would be considered good practice.
d123's circuit should also work, it uses a different principle, two timing circuits running simultaneously, one for about 6 seconds and one for about 5 seconds with the output being the difference between them.
Brian.