**Core Concept**
The patient has life-threatening hyperkalemia, a condition characterized by elevated serum potassium levels that can lead to cardiac arrhythmias, muscle weakness, and even cardiac arrest. The primary concern is to rapidly reduce the serum potassium level to prevent these complications.

**Why the Correct Answer is Right**
The patient's hyperkalemia is likely due to the combination of renal impairment from HIV nephropathy and adrenal insufficiency, which impairs potassium excretion. Additionally, the use of spironolactone, a potassium-sparing diuretic, contributes to the hyperkalemia. The immediate treatment of choice is calcium gluconate to stabilize cardiac membranes and prevent arrhythmias, and insulin/glucose to drive potassium into cells, followed by sodium bicarbonate to promote potassium excretion.

**Why Each Wrong Option is Incorrect**

**Option A:** Potassium-binding resins like polystyrene sulfonate are not effective in acute hyperkalemia and may cause intestinal obstruction.
**Option B:** Hemodialysis may be considered in severe or refractory hyperkalemia, but it is not the immediate treatment of choice.
**Option C:** Beta-agonists like albuterol can drive potassium into cells but are not the primary treatment for acute hyperkalemia.

**Clinical Pearl / High-Yield Fact**
Remember the "TREAT" mnemonic for hyperkalemia: T - Treat with calcium gluconate, R - Reduce with insulin/glucose, E - Exchange with sodium bicarbonate, A - Administer potassium-binding resins (if necessary), and T - Tailor to the individual patient's needs, including hemodialysis if necessary.

**Correct Answer:** C. Beta-agonists like albuterol can drive potassium into cells but are not the primary treatment for acute hyperkalemia, insulin/glucose is the correct answer but it is not listed, hence the best choice is to administer Calcium gluconate.