Let $X_1,\ldots,X_n$ be a random sample from $f(X;\theta)=\phi_{\theta,25}$, that is, $X_1,\ldots,X_n$ be normally distributed with mean $\theta$ and variance $25$.
I am not understanding how $$sup_{\theta\leq17}[\phi(\frac{17+\frac{5}{\sqrt n}-\theta}{\frac{5}{\sqrt n}})]=\phi(1)$$ ?
$\phi$ is unimodal, decreasing on the positive reals, and reaches its maximum, $1$, at $0$. Here, this implies that since $\theta \leq17$, the argument is positive and decreasing in $\theta$: the overall function is thus increasing wrt $\theta$, and therefore maximum at the upper boundary $17$.