We've got a Magento install that's currently running like a dog... We've had to install FPC to help with the site speed but this doesn't help with the search.
I've logged into the server and I can see the load of the server is really high and it's MySQL that's hogging it all.
Disable your FPC, then run the Magento profiler.
You're wanting to look at the 'time' column - the total of this column is your rendering time. So look for a line with a high value, this will give you the culprit.
Here's a guide that'll help you; https://www.nublue.co.uk/blog/using-magento-profiler-to-speed-up-magento-performance/
Another way is to run it on your staging server, and disable all non-default modules then re-enable them one by one.
Disable fpc, then use a profiler (like tideways, blackfire, xdebug, ...) to look into the cause and fix it.
Mostly this is some bad written code.
Afterwards, you can enable FPC again.
