In reply to rashwell:
You could have a look at Lobuje West (6145m/PD+) or Kyazo Ri (6186 m/AD). Both are in the Namche/Everest area and are easy to access.
Bear in mind the effects of the monsoon. You will find the requirements for a local guide here:
http://www.nepalmountaineering.org/noticespage-12-Climbing%20Rules
A climb for one person can easily be organised via agencies in Kathmandu.
You might consider spending more than seventeen days on this to allow for acclimatisation. This would be particularly important if you have not been above 5000m before.
Have a great trip!
Post edited at 21:58