Charge pump vs. boost converter for high current LED driver
You do not say how long between pulses in your bracket of 10 x 0.1 ms pulses - this may alter the solution (slightly easier)

Your peak power is P = I x V = 5A x 4.6V = 23 Watts.
This is not an overly demanding boost converter requirement, but even that is not essential.
Your mean power is
ton/tcycle x Pmax = 0.001/300 x 23W  = &lt; 0.1 mW = tiny.  

As long as you can store enough energy to provide the LED during pulsing you can recharge it at leisure.    

If using a capacitor as a direct to LED store then the allowed voltage droop sets the capacitor size.
C = t x i / V
t - pulse time total, i current, V allowed voltage droop 

For 0.1V allowed capacitor droop - C = (0.0001 x 10) x 5A / 0.1V = 50 mF (50,000 uF)
If you allow 1V droop then 5000 uF suffices.    

If you follow the capacitor with a 5A LDO (low dropout regulator) with say 6V into LDO then a say 10,000 uF capacitor would allow zero output droop.  



Supercapacitor:

Charged to 4.6V this 3.5F supercapacitor will drive the LED directly without an LDO being needed. Wiring drop is liable to be more than capacitor droop over 10 pulses. 

This $US3.94/1 3.5F capacitor will supply the LED with 'nary a ripple' (OK - maybe 2 mV droop over 10 pulses). It will take a few minutes to charge intially with a 5V x 0.1A  supply and thereafter recycle after each pulse train in well under a second. A 5V x 1A inverter will shorten the initial charge accoringly.

DGH355Q5R5  3.5F supercapacitor.  Pricing page.
Shortform datasheet
This 1.5F part is notionally outside its Imax spec BUT as that is for 1s your 1 ms requirement may not phase it. Or may.
It's hardly any cheaper - the 3.5F part is more attractive.