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:<
A better solution is to use the Qt SDK application "windeployqt". It is used to copy all the required dlls and plugins to your application folder based on target platform. You can then run that on another computer. Here is the documentation: https://doc.qt.io/Qt-5/windows-deployment.html.
For example, if your executable was built using mingw53_32 and your executable is in "C:\example_qtapp":
QT_INSTALL_DIR\minqw53_32\bin\windeployqt.exe c:\example_qtapp