Inspiron N5110 Memory Test failure

Test the memory modules one at a time. If one fails, move it to the other socket.  If one module fails in both sockets, replace that module with a  new one.  If both modules fail in a single socket, it's the socket that's bad - replace the mainboard.

Thank you for the answer. I tested the memory modules as you described. One of the modeles is defect and i will replace it. Generally the laptop is running very slow and overheating. A new windows installation and a format of the harddrive didn't help. I will try cleaning the fan.

Given the extensive disassembly needed to clean the fan (the mainboard has to come out), and given the position of the hard drive (it's mounted to the underside of the mainboard), you may want to consider replacing the drive and the thermal pads between the CPU, GPU and heatsinks while you're in there - the drive is getting up in age and the pads do dry out -- and the labor required to replace either of those is the same as it will be to clean the heatsink/fan assemblies.

You mean to replace the hard drive with a new one and putting some thermal paste between the CPU, GPU and heatsinks?

Yes.  In essence it's like changing the timing belt in a car - it's usually best to change the tensioners and water pump at the same time.  The added parts cost is small relative to the labor investment you're already making.

I see. But why do I need to replace the Hard Drive? The Test show that it is not defect.

Will this change the speed of the laptop?

Which hard drive will you recommend?

What do I actually need. A thermal paste or a thermal pads?

Either will work.  When you see where the hard drive is located, and consider most drives last 3-5 years at best - you may want to change the drive (or if it's performance you're looking for, replace the hard drive with a solid state drive).