I have a selenium script with python 3. I need to run it every day at 7AM for 5 minutes but I cannot leave my laptop on 24/7 just for it. What would be the easiest/best alternative?
I checked Lambda AWS but I am unable to install chrome (or the headless version of it) there and I have no experience with servers.
AWS Lambda is a viable solution for your goal - especially if the script is going to have a small runtime. They have recently increased the maximum execution time to 15 minutes, so you should be ok.
Getting headless Chrome in Lambda (in Python; it's full of JS/node.js solutions out there :)) is doable - I myself have used successfully this project in the past - https://github.com/21Buttons/pychromeless
To schedule the execution at your desired time you could use Amazon's CloudWatch.