Most Helpful Guy
Picking up new hobbies... you have to do something otherwise they'll be on your mind all the time. it's going to hurt and a piece of that person may always be with you but you have to get through it because you have no other choice... so distractions help, just so long as their healthy.
Most Helpful Girl
Feel your emotions, cry, grieve for the death of the relationship. Talk to friends if you want/have to. (This is generally the stage where I listen to all the sad breakup songs. My fav when my ex first broke up with me about 1.5 months ago was Birdy - Wild Horses once I was starting to transition into the getting over him phase, my fav song was Carrie Underwood - Starts with Goodbye because I could identify with it so much.)
Remove reminders of him from your life. Go no contact. Remove pictures of him from your phone and place them into a file hidden away on your computer. Relocate the gifts he's given you into a box in the back of your closet. Don't try to run into him. Do not stalk his social media.
Stay busy, meet new people, pick up new hobbies, hang out with friends, etc.
Then slowly, you'll find that your life is moving on without him, and that even without him you're okay. And you'll think of him less, and when you do think of him, you'll find it hurts less, until one day it stops hurting.
For me, it was helpful coming to the realization that I couldn't have changed the breakup, there was nothing I could have done. For me that was a pivotal moment where I was able to say, I gave it my all and I have no regrets, and if he gave up on the relationship, that's not my fault and I deserve someone who will be with me through thick and thin, someone who will work through problems with me.
Allow yourself time, you dated the guy for 5 years, it will take some time before you are over him.