A multi-scale morphological analysis of the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) was performed. We adapted the Metric Space Technique to perform a space-scale morphological analysis by filtering the galaxy point distributions with a smoothing Gaussian function, thus giving quantitative structural information on a range of scale sizes. The analysis was performed on 2-D (a dozen slices of a volume of space containing many newly measured galaxies from the SDSS DR5 survey) and 3-D data. Using the MST, observational data was compared to galaxy samples taken from N-body simulations with current best estimates of cosmological parameters and from random catalogs. By using the maximal ranking method among MST output functions we also developed a way to quantify the overall similarity of the observed samples with the simulated samples. MST does uncover some new multi-scale morphological properties and appears to be a good tool to measure those properties by clearly distinguishing the samples.