Then I don't know why the test code (the one at the end of the configuration tutorials on the SFML website) won't compile...
EDITI have figured it out... it was the order of stuff that was the issue. I had the libs that depended on other libs after those libs.
For people who stumble upon this thread looking for the solution, I got you fam
Here is what you add to your <Project_Name>.pro file
//Library Directories Configuration
LIBS += -L<Debug_Binaries_Base_Dir>\lib -L<Release_Binaries_Base_Dir>\lib -L<SFML_Source_Base_Dir>\extlibs\libs-mingw\x86
//Release Library Configuration
CONFIG(release, debug|release): LIBS += -llibsfml-audio-s -llibopenal32 -llibFLAC -llibvorbisenc -llibvorbisfile -llibvorbis -llibogg -llibsfml-graphics-s -llibfreetype -llibjpeg -llibsfml-network-s -lws2_32 -llibsfml-window-s -lopengl32 -lgdi32 -llibsfml-system-s -lwinmm
//Debug Library Configuration
CONFIG(debug, debug|release): LIBS += -llibsfml-audio-s-d -llibopenal32 -llibFLAC -llibvorbisenc -llibvorbisfile -llibvorbis -llibogg -llibsfml-graphics-s-d -llibfreetype -llibjpeg -llibsfml-network-s-d -lws2_32 -llibsfml-window-s-d -lopengl32 -lgdi32 -llibsfml-system-s-d -lwinmm
INCLUDEPATH += <SFML_Source_Base_Dir>\include
DEPENDPATH += <SFML_Source_Base_Dir>\include
//SFML_STATIC preprocessor definition
DEFINES += SFML_STATIC
EDIT 2This is the forum post that I found that solved my issue (for those of you that are curious)
EDIT 3I had forgotten to add the libraries for the Audio and Network modules. I also have rearranged the libs dependency libs (the ones like Freetype and GDI32) so that they are before the SFML libs that don't need them.