How to make circuit of a 32 X 32 matrix?

I have a 32 X 32 matrix show in the picture below and I want to make a circuit for this matrix. Also in the picture below to the matrix picture I have written the each column in bra-ket notation to get the idea of operators required in the circuit by seeing the qubits.

If I'm reading your matrix correctly, it can be written as $$\cos(\theta)I+i\sin(\theta)Z\otimes X^{\otimes 4}.$$ So, if I were you, I'd start by performing a rotation $$R_z(2\theta)$$ on the first qubit, creating $$(\cos(\theta)I+i\sin(\theta)Z)\otimes I,$$ and then apply four controlled-nots, controlled off each of the other 4 qubits, and targetting the first qubit. That creates $$\cos(\theta)I+i\sin(\theta)Z^{\otimes 5}.$$ You can then convert the $$Z$$s into $$X$$s using Hadamards. Overall, the circuit looks something like:
• @vardhannegi You're probably right about the sign. As you say, just flip the sign of the rotation angle, $\theta\mapsto-\theta$. Commented Feb 20, 2020 at 11:33