The Dido requirement was fleet screening

An Admiralty statement describes the small Dido-class cruiser as a reconnaissance and low-visibility fleet ship that could screen against destroyer attack and support friendly flotillas. Large cruisers presented too much silhouette and cost for this exposed work, and the requirement did not demand enough armament to fight a heavy cruiser. Its 5.25-inch battery was chosen to defeat light surface threats while also supplementing fleet anti-aircraft fire. A pure AA cruiser could have used the Royal Navy's 4.5-inch weapon, while a surface-only destroyer killer might have used a heavier gun. With 1930s technology, the 5.25-inch caliber increased shell power without making the ammunition and fast-moving mounting unmanageable. It also preserved a clear cruiser identity above destroyer weapons while sustaining the rate of fire needed against aircraft and light warships.