Sudden increase in server load at specific times

[snakes1100]

Start by removing suPHP & running apache/php as a DSO.

Then you can start checking your server logs for more details as to whats going on.

There is really no way to give you recommendations, as you havent provided much to work with in terms of settings on the server, apache, php, mysql & the OS settings for things like open file limits or if your running any caching programs etc.

Tuning a server entails much more than just simple data posted in the forums, as there are many things to look at.

Besides the fact that your server is using all its RAM & states only about 200MB free

table_cache=80000 <-- Thats way to high
max_connections=5000 <-- Way to high
open_files_limit=5400 <-- Doesnt matter unless the OS allows that many
thread_cache_size=4 <-- Wrong section & set wrong

Edit to add:
If your host is setting your server details, i would fire them on the spot for poor workmanship.......

--------------- Added [DATE]1381349605[/DATE] at [TIME]1381349605[/TIME] ---------------

Looks like you down now for server load.

Run this cmd in ssh when this happens & post the results:
netstat -plan|grep :80|awk {'print $5'}|cut -d: -f 1|sort|uniq -c|sort -nk 1