@koahnig Thank you very much for your help. Your link explained some concepts to me. I had the "The procedure entry point _ZN10QArrayData10deallocateEPS_jj could not be located in the dynamic link library Qt5Core.dll." error message and wasn't sure how to deal with it. I realized I was using only .dll files from the C:\Qt\Tools\QtCreator\bin directory. When I used the .dll files from the C:\Qt\5.4\mingw491_32\bin directory -- including libstdc++6.dll which i should have just tossed into my build folder, my issues disappeared. This makes sense since I was using that MinGW instance to do my compiling. This forum question helped my problem more specifically.
Dependency Walker is still stating that I'm missing these files:
API-MS-WIN-CORE-COM-L1-1-0.DLL
API-MS-WIN-CORE-WINRT-ERROR-L1-1-0.DLL
API-MS-WIN-CORE-WINRT-L1-1-0.DLL
API-MS-WIN-CORE-WINRT-ROBUFFER-L1-1-0.DLL
API-MS-WIN-CORE-WINRT-STRING-L1-1-0.DLL
API-MS-WIN-SHCORE-SCALING-L1-1-0.DLL
DCOMP.DLL
GPSVC.DLL
IESHIMS.DLL
These are .dll files which some forums tell me are only side problems of something unrelated.