First of all, congratulations on your tenacity to stick with it in completing your degree. It must have been a difficult road for you over those five years and it probably feels great to be finished. Commit yourself to never again sending out a resume without an intial phone call first. Always make the direct contact first. If the resume is required, follow with another phone call after delivery.
Fax is best and most immediate.
You can be back on the phone with the manager one hour later. Don't just contact the big companies. Talk to the medium and small companies. Network, network, network. Stick with it.