Check out the YAL-1.
http://en.wikipedia.org/wiki/Airborne_Laser
It can hit things far faster than MACH 5.
Intercontinental missile can not change its course during initial stage of flight that gives you time to target. Anti-ship cruise missile perform “evasive maneuvers near to the target to defeat any defenses” and that makes targeting (and keeping beam on target for several seconds) very difficult.
Read about “Yakhont” - http://www.missilethreat.com/cruise/id.103/cruise_detail.asp