Keep camera at certain distance from character when rotating

I would say try thinking your method in reverse. Instead of trying to find the distance from the camera to the player object and then applying that. You already know what distance you want, and I assume you know what position around the player you want your camera to be positioned at. So you should think about positioning the camera based on the player's location.

 //Distance away from player you want to be at.
 var distance = 10.0f;
 //Direction from the player you want to  be at.
 //Use a unit vector which can be found from any Vector3 using .Normalize
 //This vector is pointing behind and above the player at a 45deg angle
 var direction = new Vector3(-10, 10, 0);
 //distance * direction. normalized(); scales the unit vector to a constant size of distance behind the player.
 camera.position = player.position + distance * direction. normalized();

You could use the very useful Mathf.Clamp method on the camera's transform. For instance, when moving the camera you would "clamp" its position to always be at your specified distance (e.g. 5 units in your example). Mathf.Clamp in the Scripting Reference

get the slope of the line of the from the player to the camera normalize

multiply by 5 assign that to the camera

that'd be done as

 camera.transform.position = (camera.transform.position - player.transform.position).normalized * 5;

or

get the slope of the line from player to player to the camera use that as a ray so you have origin and direction

get the point 5 units along the ray ray.point(5)

assign that to the camera

mark as answered please