The power supply looks to be non regulated, and thus won’t current limit. A look at the SR506 data sheet here:
http://www.car-san.com/proditem_pdfs/doc_20110721164456.pdf
indicates here in figure 4 here
that it can take a large surge current for a short time (which should be the case here, the capacitors should charge fairly quickly I expect.) It should survive 25A for almost a second (and the power supply may not be able to supply that much current anyway!)
The problem with a resistor is that it is always there, and will drop the voltage seen by the load which is undesirable. The usual way I have heard of is to use NTC thermistors to limit the surge current. They start out with a high resistance (because they are cold) and reduce their resistance as they heat up from the current flowing through them. Another way would be to put a 5A capable coil in between the power supply and the capacitors (the coil has the opposite effect of a capacitor, it trys to keep the current constant and thus limits the surge.) The problem there is the coil is likely to be physically large (and possibly expensive). The easiest way is to just use the SR506 diode and hope the capacitors charge up fast enough to stay within the surge current limits. To that end here is a Fritzing part for a SR506 diode with the pcb pad holes set to 0.06in which should fit the pins.
edit: Replace the current part with one that has the pads spaced 0.5in apart (rather than the current 0.3in) as the diode won’t fit in 0.3in!
SR502-Schottky-Diode.fzpz (4.4 KB)
Peter