Chrome cast issues need help!!

Hi everyone!
I need help. Unsure if this is the right forum so I apologise in advance.
I have a Sony Bravia TV model # KDL40V5500 from 2009.
She’s a decent age (I know) but she’s still a great TV and I can watch movies on her through my laptop.
I decided to get a google chrome cast which has 1080HD support but my tv won’t display a picture. I’ve tried all the HDMI outlets but it won’t work. Does anyone know what I’m doing wrong? Why will it allow me to play my laptop but not the chrome cast?