Hi Vin and welcome to the group!
Sure you can upgrade to 5.x from 4.5.5, but not "straight." I recommend you follow this upgrade path. The most likely issue that you might run into is incompatibility of potential 3rd party modules. So you need to research these first before attempting any DNN upgrade.
And as always, make sure you have bulletproof backups for every step of the way.
Let us know if you have further questions and hope to see at one of our upcoming meetings.