Battery capacity and duration
Your selected battery will be good to power your light for about 1 hour of continuous work. If you fire your light for 10 seconds, your battery will last for about 360 cycles.

The total capacity rating ("5 Ah") has little relationship with how much current the battery can deliver. I would guess that your SLA battery will be able to deliver much more than 4.5A.

CORRECTION: Tony is correct, the 5AH is usually based on 20-hours discharge time. This means that to get 5AH capacity, the discharge current shouldn't exceed 250 mA. Here is an example of typical SLA 12V/5AH battery. The datasheet says that the battery will last only 30 minutes under 5.7 A load, so the battery capacity gets down to 2.85 Ah. So at 4.5 A it might last about 40 minutes of continous discharge. Impulse-type discharge, however, is more favorable, so my initial estimate of 360 bursts might be correct.

The "initial current" of 1.5A is a requirement for charging mode. And, BTW, the battery under my reference can deliver 75 A, but for a really short time of 5 seconds.