lens for surf photography (from beach)

[gckless]

Sigma 150-600 Sport may be the best lens you could get for that price for over something over 300mm, IMO anyway. The Nikon 200-500 is nice too, falls off just a bit after 400mm though.

 

[ac12]

Sigma 150-600 Sport may be the best lens you could get for that price for over something over 300mm, IMO anyway. The Nikon 200-500 is nice too, falls off just a bit after 400mm though.

Both lenses are way over the OPs budget.

OP
You should not be using VR on a tripod, so you can use older non-VR lenses, to save some $.
But I do not think your D5600 has an in-body AF motor, so you have to stick with AFS lenses.
I have not tried shooting surfing, but another option is MANUAL focus lenses. If you can follow focus the surfers. I use a manual focus 500mm on my D7200.

 

[ac12]

OP
I suggest you try renting the lens and giving it a try.
That would be much better than guessing and asking opinions of others.

Also the surf conditions and distance where you shoot may be significantly different than where others shoot.
Example a 400 might be too short for one location where the waves break further out, and too long for another location where the waves break close to shore.
Also where you site the camera affects the distance to the surfer.

You should also budget for a gimbal for your tripod. A gimbal makes tracking a moving subject with a LONG lens, much easier.

BTW you need to look at your budget again.
The Sigma 150-600 "contemporary" runs about $1,000 USD, which is $400 over your budget. The "sport" model is even more expensive.