Yes, it should be around 500 x 300 cm (or vice versa, depending on need for landscape or portrait use).
You'll have to decide what resolution to use. Using a high DPI, e.g., 300 DPI, at that size might slow your system to a crawl. If this background isn't going to be very visible or at a distance, you can definitely get away with a lower DPI, like 150.
Thank you for the quick response. It is going to be a very visible BG so I will set the DPI to max. My laptop can take it. Is there something else I might be missing? I will also use gamma 1.0. Is there a possibility the colors not to come out the way I made them inside of PS?
Considering the use, 50 ppi will be plenty. That's still a very big file at around 7900 pixels wide - or a little bigger than a native file from a Nikon D800/810. Nobody ever complained about resolution in the D810.
We need to put "300 ppi" to rest right away. That's 59 000 pixels! Trust me - that's insane.
And no, you don't set the color mode to CMYK. You ask the printer what CMYK profile they want. Remember, this will be judged against natural skin color, so color accuracy should be taken seriously here.
Actually this made me think. A very real issue here is moiré - interference patterns between the two sets of pixels (background and TV camera). You can see this with certain types of fabric. It's only a risk if the background pixel pattern is very contrasty, but nevertheless, I'd ask someone familiar with studio TV production.