Hi @Karen Arul ,
I would go for a Web Application extension's approach.
You create your internal Web Application accepting NTLM and later on you extend the Web Application for Anonymous access only.
You will then expose only the extended url to be accessible through the F5 appliance.
The reason is that critical SP services like Search for example requires NTLM authentication to work. If you kill completely NTLM you may have unexpected behavior and indeed some SP services won't work anymore.
On the counter part if you expose one single Web Application having both NTLM + Anonymous enabled, then you may have security breaches as anyone could try to enforce NTLM requests to the site by using the following:
/_windows/default.aspx?ReturnUrl=%2f_layouts%2fAuthenticate.aspx%3fSource%3d%252F&Source=%2F
Concerning the F5, I imagine you have an appliance with the WAF module installed. Based on my experience you may expect TONS of "strange" requests coming through the F5. Try to enable the learning policy so you can deep dive later and decide which Url you may want to exclude (if any)