Sleeping mysql threads?
 

Few days ago server load peaks started happening. Without really any changes on the server side, no new hacks installed or anything afaik.
Anyway I've asked support to check it out and they've informed me there is a lot of sleeping mysql threads.

And indeed few minutes ago we had another peak. Server load went to like 60.
I did mysqladmin processlist over ssh and it did indeed show a lot of threads in sleeping state.

There is usually very few of them and their time shows 0 and they go away very fast.

But when this happened there was like 50 or 60 and as I've repeated the commands their time was going up to like 6 and 7 and I assume it was same threads sticking in there.

Any idea please what could be causing this behavior ?
Or if there is any way to diagnose it?

Thanks in advance for any help.