Assertion (A) : P(3,5,4), Q(5,7,5), R(6,5,7) are the vertices of a triangle whose orthocentre is (5, 7, 5)
Reason (R) : In a right angled triangle right vertex is ethnocentric

The vertices of triangle are P(3,5,4), Q(5,7,5), R(6,5,7) 

The lengths of the sides are

 $$\begin{gathered} PQ=\sqrt{4+4+1}=3 \\ QR=\sqrt{1+4+4}=3 \\ PR=\sqrt{9+0+9}=\sqrt{18} \end{gathered}$$

Observing the above distances

${\left(PR\right)}^2={\left(PQ\right)}^2+{\left(QR\right)}^2$

Hence, the given triangle is right angled triangle

The orthocenter is the vertex at right angle

hence, the vertex at right angle is $Q$ and it is orthocenter