OK. I have too much time on my hands. I found the owner's manual (https://support.hp.com/us-en/product/hp-compaq-6000-pro-microtower-pc/4023814/model/4023815/document/c01865757), the parts and service manual (http://h10032.www1.hp.com/ctg/Manual/c01883660)
all of which tells me it has the Intel Q43 express chipset which means here are the processors it support s (for socket 775):
http://www.cpu-upgrade.com/mb-Intel_(chipsets)/Q43_Express.html
the i5-2400 does not appear to be one of them...
but here's another list--https://www.delidded.com/lga-771-775-cpus/ with current used prices for the various CPUs