This is not May CU rather it is called April 2014 CU. Due to late release of this CU cause the confusion, This package released on May 7, 2014 instead in April.
Now for the requirement after the SP1 is little change:
Be aware that all Update for SharePoint 2013 require SharePoint
Server 2013 SP1 OR March 2013 PU for SharePoint 2013 to be
Read this: http://blogs.technet.com/b/stefan_gossner/archive/2014/05/08/april-2014-cu-for-sharepoint-2013-has-finally-been-released.aspx
Now as you are on the SP1 then you dont need to the install the March PU, rather simply Install the April CU 2014.
One thing As of now, we have the October CU 2014, why not go to latest one. just one thought.
If you want to apply the October CU then you need the Sep CU 2014, due to package changes.
Also be aware that in October no so called "Server" or "Uber" packages
have been released instead only fix packages for individual components
of SharePoint have been released. That means if your SharePoint system
is on an older patch level than September 2014 CU you need to install
September 2014 CU before installing the below listed October 2014 CU
fixes in order to update your system to the latest patch level. With
other words: It is highly recommended to install SP1 and September
2014 CU before installing October 2014 CU! See SharePoint Patching
Demystified for details.