Home made USB charger based around LM2596: Smoothing caps
Yes, you can connect the output of the regulator to as many USB ports as you want, but the total current drawn by all ports can't exceed what the regulator can supply.  5 ports is really pushing it unless you know that the devices that you will be charging don't take much current.  Normal USB ports only guarantee 100 mA, and then up to 500 mA after negotiation.  However, the pure charging interface doesn't require any negotiation and can supply significantly more.  Note that the LM2596 only guarantees 3.6 A.

Yes, you need a capacitor on the output of a full wave bridge.  It sounds like you plan to feed the LM2596 from the full wave rectified output of a transformer secondary.  That's fine, but the reservoir cap is still important.  Without the cap, the voltage will drop to 0 twice per line cycle.  You need a big enough cap so that the minimum input voltage of the LM2596 is maintained between power line peaks when the cap will be recharged.

For example, assuming 60 Hz power, there is 8.3 ms between line cycle peaks where the cap gets charged.  With a 3.6 A load, a 10 mF cap would drop 3.0 V.  If you have at least that much headroom above the regulators minimum input voltage, then that's fine.  One nice characteristic of such a switching regulator is that it can handle a wide input voltage range.  This one can handle up to 40 V.  If you can arrange the transformer output after the rectifiers to provide nearly that much under no load, you have a lot of room to allow the voltage to sag between peaks and can use a smaller cap than 10 mF.

If you really want to drive a large number of ports, you could use multiple regulators, in which case the total current required out of the transformer will be higher and the cap will need to be larger to achieve the same voltage drop.