I have written a program with Qt5.3.1 and run it on my development machine where it works fine. I copied all necessary .dll files into the folder where my .exe is. These are:<
You should place Qt DLLs along the release version of your executable. These are Qt5Core.dll, Qt5Gui.dll and possibly the ones for other modules that you have used. These dll files are in your installed Qt Directory in bin folder. You should also place LIBGCC_S_DW2-1.DLL, MINGWM10.DLL and LIBSTDC++-6.dll in case you are using MinGW.
If you are using plugins you should place their dll in a folder named plugins beside your exe. In case of using icons and images you should ship their dlls like qico.dll and qsvg.dll in a folder named imageformats.