It was cooling fine until about 3:00pm today. Fan is running, just luke-cool air. Outside unit is not running, it kind of clicks and hums periodically but does not come on. Unit is a Carrier 5 ton unit about 8 years old. I left it off from 5pm to 1am, still no change.

Any ideas on trouble-shooting it?

Id bet it is a bad capacitor in the outside unit, one way to find out, if you can spin the fan in the direction it runs and it takes off, then it is almost certainly a run/start capacitor.
They are relatively cheap to change yourself, finding one in a timely manner could be a PITA. They go out enough that I keep a spare bought off Amazon.

BTW, look on youtube on how to discharge a capacitor, before handling one, they will/can hold a charge.

Agree with Dennis

Thanks, gents, I will check it out!

It's an odd size,70/7.5

If you have an ac, or electrical supply in town, call them in the am and you will probably get going. Or, you can google the one you have and get one sent quick from Amazon, I would get a spare.

My ac had a single 3/4 pole run/start for pump and fan, 1st time it went out, it was changed to 2 separate cap's, one for fan, one for pump. I have spares for both and also got one for the inside fan , there is one there as well.

A visual inspection...

Most blown caps are swollen, rounded on bottom or the terminals on top are not parallel (90 degrees from case) indicating the case is swollen on top.

If none of these are present, being a carrier, might want to call a dealer.
Depending on your urgency.

70 7.5 is norm for carrier 5ton.

If you need a cap and go the DYI route. You get What you pay for. Cheap caps will not last long. Get one made in here not china.

If it is low on Freon it will also click and hum. Outside fan will run but compressor will not run if low on Freon.

I keep spare caps on hand. You can get them reasonable on Amazon or eBay. That way if one goes out on a weekend or late evening, you have one to replace.

I got a new capacitor and installed it but the outside unit would still not come on. Called an AC company, guy checks it all out, can't find anything wrong, can't get it to cool. He finally notices that one little wire that he says is part of the heating system is unplugged from the board. He plugs it back in, next time we try the unit it works just fine. He claims that shouldn't have done it. Now I don't know if somehow that wire came off or if I truly had a bad cap the first go-round.

Thank you all for your help.

Gotta love Carrier's - I'm been trouble shooting an issue with my upstairs unit for a couple weeks. Thought it was a capacitor; AC guy said it was the fan motor; replaced the fan and still doesn't work. I hate my Carrier units. I will say though I went on Amazon and bought a spare for each capacitor on my units. Cheap insurance for an easy fix in the event the cap is the issue.

My carrier blow motor went out few weeks ago... got to cut another hole for a filter screen since the 25,16,1 is to small for the 4 ton i got

No local folks delt with carrier either i had to get a company from BCS to come out...

My American Standard did this a while back (outside fan and air handler working, but compressor wouldn't kick on)

AC drain was clogged and float switch was activated and wouldn't allow compressor to kick in