Q: Transferring photos from new iPhone to old Mac is possible but how?

It isn't in your post but since you posted from an AirDrop support page, note that AirDrop between a Mac and an iOS device will only work with a 2012 or later model Mac. See the following from Mac Basics: AirDrop lets you send files from your Mac to nearby Macs and iOS devices - Apple Support

In order to transfer files between a Mac and and an iPhone, iPad or iPod touch

• your iOS device needs to include a lightning connector
• your iOS device needs iOS 7 or later installed
• your Mac needs to be a 2012 or later model with OS X Yosemite installed
• Your Mac and iOS device both need bluetooth and Wi-Fi turned on. You do not have to be connected to a specific Wi-Fi network.

You can transfer without AirDrop via USB cable, via 3rd party apps such as PhotoSync, via PhotoStream, via email, etc.

I have a MBP (mid-2010) with OS X El Capitan recently installed, and i also have an iPhone5 with iOS9 installed, i can't send any item from the iPhone to the Mac? i have to use a 3rd party app or USB cable???

I would use the USB cable that came with the iPhone.  Then you can import the photos into your iPhoto library or use Image Capture (located in the Applications folder) to import the photos into a folder on the Desktop. 

tute420 wrote:

 

I have a MBP (mid-2010) with OS X El Capitan recently installed, and i also have an iPhone5 with iOS9 installed, i can't transfer photos from iPhone to Mac? i have to use a 3rd party app or USB cable???

I recommend that you use the USB cable to transfer via iTunes, Import photos and videos from your iPhone, iPad, or iPod touch to your computer - Apple Support or you can:

1. use cloud drive like Dropbox, One Drive. Upload your photos from iPhone to cloud and download on your Mac.

2. use iCloud app sync your photos to your Mac.