**Core Concept**
The patient's symptoms are indicative of a third cranial nerve (oculomotor nerve) palsy. The oculomotor nerve controls the movement of the eyeball, eyelid, and pupil. Damage to this nerve can lead to ptosis (drooping eyelid), lateral and downward deviation of the eye, and pupillary dilation.

**Why the Correct Answer is Right**
The oculomotor nerve (CN III) originates from the midbrain and has three main branches: the superior division supplies the levator palpebrae superioris, the medial rectus, and the inferior oblique muscles; the inferior division supplies the medial and inferior rectus muscles, the inferior oblique muscle, and the ciliary ganglion; and the nasociliary branch supplies the ciliary ganglion and the ciliary body. The patient's symptoms, including ptosis, lateral and downward deviation of the eye, and pupillary dilation, are consistent with a left oculomotor nerve palsy, as the nerve is responsible for the motor functions of the eye.

**Why Each Wrong Option is Incorrect**
**Option A:** The trochlear nerve (CN IV) is responsible for innervating the superior oblique muscle, which is involved in eye movement but not responsible for the patient's symptoms.

**Option B:** The abducens nerve (CN VI) controls the lateral rectus muscle, which is involved in outward eye movement but not responsible for the patient's symptoms.

**Option C:** The trigeminal nerve (CN V) is a mixed nerve responsible for sensory and motor functions of the face but not responsible for eye movement.

**Option D:** The facial nerve (CN VII) controls facial expressions and taste but not eye movement.

**Clinical Pearl / High-Yield Fact**
A third cranial nerve palsy can be caused by an aneurysm of the posterior communicating artery, a tumor, or an ischemic event affecting the nerve. The patient's symptoms should prompt a thorough investigation to identify the underlying cause.

**Correct Answer:** C. The oculomotor nerve (CN III).