I have pretty much the exact same laptop. (HP DV5-2035dx)
I found the solution to making the touchpad work was to add the uTouch PPA. Once the PPA was added, install the synaptics-dkms package. Reboot, change to two-finger scrolling, and it works great.
I will walk you through the easy installation.
1) Add the uTouch PPA by pasting the following into terminal.
2) Update repositories, and install the synaptics-dkms package.
sudo add-apt-repository ppa:utouch-team/utouch
3) Reboot your laptop.
sudo apt-get update && sudo apt-get install synaptics-dkms
4) Go to System > Preferences > Mouse. Go to the Touchpad Tab, and click two finger scrolling. Click the close button.
Now you are ready to test your touchpad.
What do you think? Much better?
If you aren't satisfied with the results you can simply remove the package by opening up terminal again and paste this in.
sudo apt-get remove synaptics-dkms