We have 5 double outlets connected on one circuit. Now we noticed that if we connect outlet tester to any outlet it's indicate 'correct', but if we plug appliance to any one of outlets in the circuit, the tester starts to shoe 'open ground'. It happens with every outlet that we tested and any outlet we connected appliances to. We checked the tester with other outlets in the house and it works fine. We already tried to open all the outlets and tighten the wires. Does anyone have any ideas on what's going on? Thanks
Stop. Stop worrying about the silly message from a $3 tester.
We call them "Magic 8-ball" testers
Because like the magic 8-ball, whatever answer is stated on the legend is an amusement at best.
The style of these testers is to have 3 lights and a litle "legend" that tries to interpret the lights. Worse, newer testers embed a little computer that changes what the 3 lights mean! On the originals, the lights are semi-useful if you understand what they are indicating and how to interpret half-lit lights. (And your tester is built well enough you don't see bleed-through between lights). The legends were always useless. one is in my toolbox for the lamps.
I don't know if your tester is an "at least the lamps are ok" ones or not. Assuming that it is, and you are getting two yellows and one yellow extinguishes with a big load attached.... But the load works.
It might be exactly what it says on the tin, a weak neutral-ground bond, but with these, it usually isn't.
It sounds like the 5 receptacles are hooked together properly, so I would look upstream (toward supply). Either a sixth outlet* you don't know about, or the panel itself.
To start, run this test on another circuit and see if it also does it. That would make it a full-panel problem and we can just go there.
Then shut off this circuit breaker and scour the house for any outlets* that went dead. Obviously those would be on the same circuit, and their box is worth looking inside for anything out of order.
Next go to the panel and scour the safety Equipment Grounding Conductor system in your panel for anything amiss. Making sure all the grounds are on the ground bar.
If the panel is a main panel: it's the first panel past the meter, neutrals and grounds are spammed onto the same bar. Inelegant but legal because of the next step.
Next, we need to go to the main panel/breaker and look at the Equipotential Bonding System. This is simpler than it sounds: it's a fat wire between neutral and ground bars in the main panel only. This can't be too beefy. Sometimes this is a magic green screw in the neutral bus that screw into panel chassis. I have seen those fail. I prefer a beefy #4 bare wire from neutral bus to ground bus or chassis. When I say One Place I mean the one main panel. Redundancy inside that panel is permitted.
Neutral and ground must not be bonded anywhere else.
Lastly we can declare the grounds "golden" once we look at the Grounding Electrode System - but that isn't involved in this problem.
If you have an older subpanel that only has a 3-wire connection (hot-hot-neutral) then you may see grounds on the neutral bar in that subpanel. That is obsolete and a bit dangerous. You are allowed to retrofit just a ground wire back to the main panel, and separate neutral and ground in that subpanel, as is normal for new work.
Back to the branch circuit
If you found any grounding system defects, that should lick it. If not, we have to go back to the branch and check it through-and-through for defects. I assume you've a) already been doing that, and b) doing it correctly, so at this point the most likely failure point is b). Re-educate on how to do this stuff, and take another look.
* an "outlet" means any point-of-use for electrical power, not just receptacles.
Extremely experienced and skilled people can sometimes figure out weird results like this before making any tests, but the rest of us have to start trying possibilities. If you have a VOM, you could use the resistance mode to see if the ground is truly open. You would put the probes into the neutral slot (longer one) and the ground and determine the resistance with and without an appliance that causes the tester to show "open ground". Any reading above ~0.4 Ohm between neutral and ground could indicate a problem with the ground.
First use the meter in the voltage mode to make sure that the slots you are going to probe in the resistance mode are not hot.