Hello FloortjevdV,
I saw that your Photosmart 5524 is not responding to you when you press the power button but will power on if you are to unplug and plug it back in.
I have searched for this type of power issue and I have found a troubleshooting document that I recommend you follow.
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01321436
If the troubleshooting does not resolve the issue, I suggest calling HP's Technical Support to see if there are any other options for you. If you are under warranty, you may qualify for a replacement part or unit.
HP's Contact Info: http://www8.hp.com/us/en/contact-hp/ww-contact-us.html
Best wishes,