Answer:
Yes, it is a quadratic equation.
Explanation:
Let's solve it to make it a quadratic equation:
=>

=> x²+1 = 5x²
=> 5x²-x²-1 = 0
=> 4x²-1 = 0
Comparing it with the standard form of quadratic equation i.e.

So, we get
a = 4 , b = 0 and c = -1
So, yes. It is a quadratic equation and it is a pure quadratic equation since b is equal to 0.