Are there coprime nonzero integers $u,v,w$ such that $2u(u^2+pv^2)=w^p$ where $p>3$?

Question

Let $p$ be a prime.

Let $u,v$ be coprime non zero integers,$w$ is an integer. Does the equation $$2u(u^2+pv^2)=w^p$$ always yield an infinite descent argument?

For some primes like (3,7), it is evident. It does not look too evident to me for some other primes like 5. Any hint will be very much appreciated. Thanks.