For which blocks is there a difference in actual mining speed between diamond pickaxe with efficiency 4 and 5?

Solution 1:

• with Haste II (from a beacon), the difference is crucial: stone, granite, andesite, diorite can be insta-mined (1 gametick/block so 20 blocks per second). No so with Eff4.
• Terracotta can be insta-mined with Eff5 and Haste I (using beacon with small base or a conduit).
• there will be a small difference for nearly all blocks that take longer than 0.4s to mine with an eff4 pick (but pick is the right tool to mine them). That includes obsidian, endstone, ancient debris, nether brick, enderchests, also a lot of more common blocks in situations when mining speed is reduced (under water, levitating, swimming, under mining fatigue, hanging in cobweb, etc.) There are some exceptions e.g. mining speed of iron blocks remains reduced the same amount.
• for great most blocks that can be mined in 0.4s (cobble, stone, and generally majority of building blocks) without haste there is no difference.

Essentially, any speed improvement that would result in breaking time shorter than 0.4s but longer than 0.05s (instamine) gets capped at 0.4s. In practice, that means the difference will be minor for players mining obsidian, endstone and nether brick, crucial for users of beacons, and mostly insignificant for the rest.