You can extract a Dem from satellite imagery (http://earthexplorer.usgs.gov/). However these images have 30 meters pixel. You cannot find easily higher resolution.
Another approach is to use gdem data (http://gdem.ersdac.jspacesystems.or.jp/). The accuracy is about 20 meters, read the documentation provided.
But what do you expect ? you cannot find 5 meters dem for free. You can contact also your university to check whether there are some data from previous project.