Yes, I am sure, that's why they made an specific power supply for raspberry pi 5 that does not follow the USB PD standard as I mentioned in my first post, and that's why I think a regular cable or adapter in the middle, if it is embarked, might not allow the 5A. But as said, I don't know, it is just my hypothesis, and if the cable/adapter is not embarked, itight work perfectly fine.
EDITED
Reading through the specification, 3A appears to be a minimum current for a rated power over 15W. Under Table 3.2 the maximum current is defined as:
• 5V, 9V, and 15V SPR Fixed PDOs
• PDO Maximum Current = Minimum( 3A, Port Present PDP ÷ Fixed PDO Voltage )
If the Port Present PDP is 25W and the Fixed PDO Voltage is 5V, the maximum current is 3A or 5A.
Also, using a Variable power data object (PDO) or a Battery PDO, higher current capacity is allowed. (Higher current capacity also is allowed for a Fixed PDO, but 3.2.5.1.4.a seemingly still limits 5V to the above calculation.)
Specifically, section 3.2.5.1 states the following:
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In addition to the voltages and currents specified in Section 3.2.4, an SPR Source May Optionally supply additional voltages and increased currents.
While allowed, the use of Optional voltages and currents is strongly discouraged to avoid user confusion. Optional voltages or currents allow Sinks that might perform differently with a Source with an Optional voltage or current than with a Source with an equivalent Port Maximum PDP but without the Optional voltage or current.
The following are Requirements apply to Optional Fixed, Variable, and Battery PDOs:
...
4. A Source May offer a Variable PDO, a Battery PDO, or a higher Maximum Current in a Fixed PDO than that found in Table 3.1 and Table 3.2. The following Requirements apply:
...
c. A Source Shall Not Advertise a Maximum Current for a Variable PDO that would result in the maximum power for that PDO (Maximum Voltage × Maximum Current) exceeding the maximum power (1.05 × Voltage × Maximum Current) of the next higher voltage required Fixed PDO (5V, 9V, 15V, or 20V) as specified in Table 3.1 and Table 3.2. The 1.05 factor accounts for the ±5% voltage tolerance of Fixed PDOs.
d. A Source Shall Not Advertise a Maximum Power for a Battery PDO that would result in the maximum power for that PDO exceeding the maximum power (1.05 × Voltage × Maximum Current) of the next higher voltage required Fixed PDO (5V, 9V, 15V, or 20V) as specified in Table 3.1 and Table 3.2. The 1.05 factor accounts for the ±5% voltage tolerance of Fixed PDOs.
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The next higher voltage following 5V is 9V. For 9V, let's make it easy and use the 3A minimum current instead of the 9V maximum current. 1.05 x 9 x 3 = 28.35W. 5V at 5A is 25W, which does not exceed 28.35W, and thus is acceptable.
All that being said, I doubt there is a suitable power supply other than the specific one offered and, if there is one, it probably is unique and very expensive. I think that is why there is a specific power supply for the Pi 5, but I don't see why it wouldn't comply with the USB PD - I don't know whether it does or doesn't.