If you built it with
make in the root directory of the source, you should find it at
/home/me/Desktop/SDL/SDL2-2.0.5/build/.libs. If you used CMake, it should be in that directory where you built it.
If you don’t install the library into the default library search paths, you can use the
-L option to tell g++ where to look:
-L/home/me/Desktop/SDL/SDL2-2.0.5/build/.libs. You also need to tell the dynamic linker where to look with the
LD_LIBRARY_PATH environment variable:
ldd if it got picked up correctly.
This will print the library paths it will use for your program.