5V source directly or 12V stepped down to 5V
TLDR:
If the problem is DC drop, then use the 12V line and have a voltage converter at the load. Also minimize the cable length.
If the problem is AC droop you'll need decoupling capacitance. Not just 1 big cap but several caps due to the impedance profile of caps.
Explanation:
The &quot;Power Source&quot; is not the ATA cable, it's your PSU. I will assume that your PSU is capable of supplying the amount of power required (i.e. VxI). There are several reasons why the voltage drop might be happening. Also, I'm not sure if you're talking about a DC drop or an AC droop so I'll answer for both.
DC Drop:
No amount of capacitance will help your DC drop. As you may be aware, DC drop is due to IxR. Capacitors are used to battle AC droop when your regulator bandwidth is not high enough. If your ATA cable is too long, that's a problem because it adds both inductance and resistance in the line. How do we combat this? Well, at the end of the day you're delivering power not current and power is nothing more than VxI. If your ATA cable is too resistive (i.e. too long) then we you could use your 12V line instead of 5V because as you increase the voltage the current will drop to deliver the same amount of power. This will minimize DC drop. Also, a shorter cable might help.
AC Droop
Capacitors store energy that can be delivered to the load when the regulator bandwidth is not fast enough. However, most people make the mistake of thinking that a very big capacitor will solve their problem. This is not the case due to the impedance profile of the capacitor (see below). Capacitor impedance decreases with increasing frequency (1/jwC). After a certain frequency the capacitor exhibits the impedance of an inductor (jwL). This means the capacitor's impedance increases with frequency. Furthermore, the capacitor has a minimum resistance ESR from it's wires. Without knowing you dI/dt of your load (i.e. the frequency) it is good practice to assume it varies. Therefore, always use several capacitors in parallel of varying magnitudes to minimize the impedance profile across frequencies.
The conclusion should be apparent. Use the technique of parallel capacitors for decoupling but also use your higher voltage line to minimize current (i.e. IR drop) and then use a converter close to your load.

Images from: https://poulpetersen.dk/notes/cimp.html

Images from: https://techweb.rohm.com/knowledge/emc/s-emc/03-s-emc/7669