deploying apm gtm asm and ltm on one box 5000 series

In my opinion, they are all good combinations in two's. ltm-apm, ltm-gtm, ltm-asm but combining them means you are performing multiple roles on the one device.

ASM is a WAF, web application firewall used to protect applications setup inside LTM. It is CPU hungry so thats a consideration.

APM is generally used as an access gateway which means your LTM would need to be connected to the edge of your network.

GTM is generally used for external DNS (internet facing services) so it would be essentially on the Internet.

Your security posture may end up playing a role in what you want to run. I would suggest LTM,APM,GTM or LTM,ASM combination. The 5000 series is just overkill for GTM which is usually at the front door with LTM/AFM protecting the data centre. But its all subjective opinion and without really knowing what your goals are it is very difficult to make accurate suggestions.

Your requirements will drive the decisions.