How to attach files to node instead of uploading? I have 2 content types, Files and Events. Files content type is used to upload files like Image, PDF, Doc etc. 

Events content type has a field to attach a document which is uploaded by files content type. The requirement, in event content type I need a field called 'attach files' with maximum five attachment. On click of 'attach files' button, needs to open a page which lists all files uploaded by files content type. On hover of any files an attach button will appear and while clicking it will get attached to the event newly creating event node.
Try the Attachment Links module

The Attachment Links module provides permanent links to files attached to a node. A single, easy-to-remember URL can be used to retrieve the preferred (canonical) or newest version of a file regardless of how many versions of that file have been attached to a node.
Typically, users will want to create a &quot;File&quot; content type and enable the Attachment Links module for that content type. Each &quot;File&quot; node should refer to a single file: &quot;Handbook,&quot; &quot;Company logo,&quot; &quot;Team roster,&quot; etc. Though each node could contain multiple versions of the file, Attachment Link provides permanent link to access the preferred or newest versions.

It seems you can also use the IMCE for FileField module to get the uploaded files from other content type. check this answer  posted by me.