A 5yo HP laptop will have no problem with any Linux flavour. It will be like night and day with an old Windows installation.
If you have a USB stick big enough (1gb up I think), you can download a few distributions (Xubuntu, Fedora, Linux Mint ‘cinnamon’ and ‘Mate editions)… and burn them onto your stick with a free program called Unetbootin. You can then boot your PC from the stick and try the different distributions without installing anything. Though bear in mind an installed operating system will always run faster than one which is on a USB stick.
Ubuntu has a user interface that many hate – I’m not a fan so would definitely recommend you at least try Mint Cinnamon and Xubuntu. Download the Long Term Support edition if you don’t want to have to do it again til 2017, the newer releases ‘expire’ in pretty short order.
I am using an oldish Pavilion with Fedora 19 and it’s grand, I never used the Windows it came with, wiping it on the first boot…