Hopefully a forum member has the DSC system.
The simple answer is:
IF the 5580 sends X10 control signals to the powerline, yes it should control X10 modules (Wall Switches, Appliance Modules, Lamp Modules, etc) , baring the typical Noise, Phase coupling, Signal sucker problems that sometimes interferes with X10 powerline signals. These "hinderences" are all solvable.
This post below indicates the DSC system requires a X10 interface to actually couple the X10 generated control signals from the DSC system to the homes powerlines.
http://forums.x10.com/index.php?topic=8357.0. The post indicates the installation was problematic.
Also if the DSC provides a closure upon alarm, that closure can be coupled to a X10 "Power Flash" which will in turn send out a X10 House Code, Unit Code ON signal on the powerline. When the closure goes away the Power Flash sends a HCUC OFF signal. Any X10 or X10 compatable module will respond if set to the same HCUC.
Go to X10.com and Smarthome.com for all the available X10 modules.