Q: So, I can not connect a matchbook pro 13 mid 2010 using Yosemite, with an iPhone 5S, via Airdrop?

Correct.

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To determine if your MBP is capable of supporting the Yosemite incarnation of AirDrop, click in your desktop field so that "Finder" appears next to the black Apple icon (left end of menubar). Now click on the "Go" menu. Is AirDrop listed? If not, it is not supported.

In this thread:

Re: Airdrop between Macbook Pro and iPhone 5 not working

it appears that Apple made changes in AirDrop with Yosemite that left some older Mac models that once supported it now incapable of doing so.

These system requirements suggest your 2010 model is too old:

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.

That is from this Apple article:

Mac Basics: AirDrop lets you send files from your Mac to nearby Macs and iOS devices - Apple Support

Your computer supports AirDrop with another Mac; installing Yosemite didn’t change this. It doesn’t support it with an iOS device.

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