Does flashing Factory image on nexus 5 reinstall core apps I messed up with some internal core apks of nexus 5 running 5.1 (android L) to be particular Google play services.

I want to get back the original apks. Would flashing factory image help me with that ?
Go to settings>apps and scroll down to Google Play Services. You can uninstall updates from there. And yes, flashing the factory image would help, but is probably overkill for your problem.