Cannot access Recovery Mode on Mac OS X
The original A1278 MacBook Pro unibody was shipped with Mac OS X 10.5.5 (Leopard).

From MacTracker


  OVERVIEW
  
  Introduced    October 2008 Discontinued   June 2009 Model
  Identifier    MacBook5,1 Model Number A1278 EMC   2254 Order
  Number    MB466LL/A (2.0 GHz), MB467LL/A (2.4 GHz) Initial Price  $1,299
  (2.0 GHz) $1,599 (2.4 GHz) Support Status Vintage Case    Precision
  aluminum unibody Weight and Dimensions    4.5 lbs., 0.95" H x 12.78" W x
  8.94" D PROCESSOR
  
  Processor Intel Core 2 Duo (P7350, P8600) ("Penryn") Processor
  Speed 2.0 or 2.4 GHz Architecture 64-bit Number of Cores  2 Cache 3 MB
  on chip shared L2 cache System Bus    1066 MHz STORAGE AND MEDIA
  
  Storage   160, 250, or 320 GB (5400-rpm SATA) or 128 or 256 GB (SSD)
  Media Slot-loading 8x SuperDrive (DVD±R DL/DVD±RW/CD-RW) KEYBOARD AND
  TRACKPAD
  
  Trackpad  Multi-Touch trackpad Keyboard   Full size (78 (U.S.) or 79
  (ISO) keys incl. 12 function, 4 arrow). Illuminated keyboard on 2.4
  GHz


You may find some useful information in this thread.  The MacBook you have was shipped with a DVD that contained the installation and recovery files.  Whether or not you have access to this DVD, you will have to purchase OS X 10.6 Snow Leopard from Apple in order to upgrade to the latest supported OS which is 10.10 Yosemite.

Apple Support:


  Upgrading from OS X Leopard If you’re running Leopard and would like
  to upgrade to OS X Yosemite, first you’ll need to upgrade to OS X Snow
  Leopard. You can purchase OS X Snow Leopard here.


While Yosemite is a free upgrade Snow Leopard still carries a $19.99 USD price tag.  See Apple's Upgrade Support page for details.

Depending on your investment, the price may be worth considering.

See also this answer:


  Can I download Mac OS X for a used MacBook Pro?