Can the LM2587/LM2588 handle a 5A load since it is rated at 5A switch current?
No. In the Boost topology design, the output load current and the switch current are not equal The maximum available load current is always less than the current rating of the switch transistor. The maximum total power available for conversion in any regulator is equal to the input voltage multiplied by the the maximum average input current (which is less than the current rating of the switch transistor). Since the output voltage of the Boost is higher than the input voltage, it follows that the output current must be lower than the input current. The easiest way to determine the necessary switch current rating (and the appropriate boost/flyback regulator IC) is to use the online design tools of National”s Power Webench, or the offline design tool of “Switchers Made Simple”. One way to get around this limitation is to use flyback topology with an external power transistor to boost the load current handling capability of the converter.