The answer is nuanced. It can run workloads somewhat faster and cooler than Pi 4 without active cooling. But it also can't reach close to its peak performance without active cooling.
"The combination of a newer core, a higher clock speed, and a smaller process geometry yields a much faster Raspberry Pi, and one that consumes much less power for a given workload."
The actual info I'd rely upon at this point:
https://www.phoronix.com/benchmark/result/raspberry-pi-5-coo...
pi5 with active cooler is about 1.2-1.5x faster than pi5 without cooler for most workloads that care than without.
Pi5 with active cooler is about 2-2.5x faster than Pi4. So Pi5 without cooler is probably about 1.5x faster than pi4, depending upon workload. (And more than this for quick bursts where thermal mass wins).
But it makes wonder how much more phone manufacturers could squeeze out of their phones, although Apple are definately overclocking the 15.