Copying libEGL.dll
from Qt should resolve the GPSVC.dll
and IESHIMS.dll
dependency issue (has for me in the past). However you will encounter issues with qt 5.0.1 and GCC 4.7, as they are incompatible. Qt 4.8 is however compatible with GCC 4.4, and QT 5.2 is compatible with GCC 4.8.0, either of which will ensure a more trouble-free compilation:)
You may have to incorporate the msvc2010 c++ distributable package from 32 bit download or 64 bit download before your app can run independently
Also, for release version of QT apps you may well have to build your own QT from source, as the distributed version only used to include support for debug mode (as discussed here
There are also some trouble-shooting guides at paulnettleship.com which, whilst they require some changes to point to the right directories for more modern versions than Qt 4.7, are still nice, short useful reference guides.
Another good guide to compiling your own Qt (VS again)is located here, whilst there is a Qt MinGW guide here which gives a walkthrough of how to compile Qt Desktop using minGW. There is another (in my opinion) more straightforward guide at http://wiki.batcom-it.net/ which walks through the actual build steps and is quite reasonably updated.