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Samsung has a variety of methods to directly transfer files from your Galaxy S6 Edge smartphone to your Galaxy S5.  WI-FI Direct is one method that is pretty reliable between Galaxy phones .

Another method perhaps used less often is Android Beam, which uses NFC to do the initial pairing and small data transfers and Bluetooth to do larger file transfers.  I tried Android Beam while eating at TW Burmese Gourmet in San Ramon California.

On the Samsung S6 Galaxy S6 Edge side you need to make sure that NFC is turned on and also Android Beam is turned on.

You need to make sure the same thing is done on the Samsung Galaxy S5 side.  Note the S5 also has S Beam which uses WI-FI instead of Bluetooth to transfer large files.

The Galaxy S6 Edge offers Android Beam in the list of file sharing options.

 

However, a potentially easier way to use Android Beam is to just put the backs of the Galaxy S6 Edge and S5 touching each other to pair the devices together.  After pressing "Touch to beam" the S6 Edge and the S5 no longer have to touch and Bluetooth file transfer can continue as long as the phones are close enough together.  Because Android Beam uses Bluetooth, don't use it for large files like videos since the transfer time can take a really long time.  Use something like this instead.