If you run the following commands all the dependencies will be resolved (it will also install libapache2-mod-php5). You can read about LAMP install in Raspberry Pi in the chapter 8 "A LAMP of Your Own", of the book "Learn Raspberry Pi with Linux", by Peter Membrey and David Hows, Apress, 2012.
$ sudo apt-get install mysql-server
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following extra packages will be installed:
heirloom-mailx libaio1 libdbd-mysql-perl libdbi-perl libhtml-template-perl
libmysqlclient16 libnet-daemon-perl libplrpc-perl mysql-client-5.5
mysql-common mysql-server-5.5 mysql-server-core-5.5
Suggested packages:
libipc-sharedcache-perl libterm-readkey-perl tinyca
The following NEW packages will be installed:
heirloom-mailx libaio1 libdbd-mysql-perl libdbi-perl libhtml-template-perl
libmysqlclient16 libnet-daemon-perl libplrpc-perl mysql-client-5.5
mysql-common mysql-server mysql-server-5.5 mysql-server-core-5.5
0 upgraded, 13 newly installed, 0 to remove and 84 not upgraded.
Need to get 9,770 kB of archives.
After this operation, 91.5 MB of additional disk space will be used.
Do you want to continue [Y/n]?
...
$ sudo apt-get install php5
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following extra packages will be installed:
apache2-mpm-prefork libapache2-mod-php5 libonig2 libqdbm14 php5-cli php5-common
Suggested packages:
php-pear
The following packages will be REMOVED:
apache2-mpm-worker
The following NEW packages will be installed:
apache2-mpm-prefork libapache2-mod-php5 libonig2 libqdbm14 php5 php5-cli php5-common
0 upgraded, 7 newly installed, 1 to remove and 84 not upgraded.
Need to get 5,707 kB of archives.
After this operation, 16.3 MB of additional disk space will be used.
Do you want to continue [Y/n]?