Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles?

Ok, from the link given by @count_to_10, I think the answer is clear from this response:

You can launch from a dead stop at any RPM you want, whereas from 5 MPH it's assumed the car is already in gear at low RPMs.

When you start from a standstill, you can rev the engine to any RPM you like before throwing the clutch to engage the axle. Maybe you could match the static friction of the surface to achieve the maximum possible acceleration. When they start at 5 mph, another answer on that site makes it clear that they assume your RPMs are matched to your motion:

"What about rolling at 5mph and dropping the clutch like a regular launch? Wouldn't that help?"
Yeah, but that's not how they test 5-60 or any other rolling acceleration tests. That's the point of them: to test how much passing power you have while already rolling, in gear without a clutch-drop.

So the engine has to move through the entire range of RPMs, which takes more power.

In the rolling start there is no tire slip or revving on the engine and so the run starts at low rpm where the engine is making less power.

A rolling start might have the engine at 2000rpm making for example 200 lb-ft (or 76hp) resulting in 0.45g of acceleration at 5mph (this example yields the acceleration to be 0.002253 times the torque produced).

With a launch from zero the engine is revved first then its kinetic energy transferred to the car yielding the first 5 mph almost instantaneously. At this point the clutch is either still slipping, or the tires spinning allowing the engine to be at about 4500rpm. The higher engine speed and the slightly higher torque (like 220 lb-ft) results in significantly higher engine power at about 188 hp (Power = Torque × RPM/5250). Some of this power is lost due to the clutch/tire slipping so the wheels see like 50%-60% of it, or 113 hp. At the same 5 mph this power at the wheels means about 0.67g of acceleration (or 0.0030 times torque produced) or 35% more.

In summary,

  • Rolling start: Engine bogs down and it takes time to get up to the "power band". Peak acceleration decided by engine torque only.

  • Launch: Keep engine spinning in the "mid range" and slip clutch or spin tires enough to match available traction.

This is not so much a question of physics as it is a question for mechanics.

The 0–60 mph benchmark is commonly quoted in publications for car enthusiasts. As with any benchmark, manufacturers will try to game the system. Fancy sports cars have launch control systems: if the car starts from standstill and the accelerator is floored, then special programming kicks in, with extremely aggressive shifting and engine tuning, without regard for usual considerations such as longevity and emissions.

Basically, it's a bit like Volkswagening a test, but less evil since the test case rarely happens in real life. Arguably, if the tuning technique achieves the desired result of maximizing acceleration at any cost, then it's not cheating.