Yes
I have advice but first how about some pics. I need to see the type of cracks the wall has and the proximity of the palms as well as the type they are.
Palms have thousands of roots the size of your fingers. They put pressure on things like push on walls and lift when under them.
I usually say no closer then 1m (3') to the edge of the palm trunk not the middle.
Watch this video. WMV 10.7mb
http://www.palmtreeservices.com.au/video/palmroots.wmv
Important question, what was there first, the palms or the wall?