Now I detect motion with my Arduino Nano and 3pin (SIGNAL, 5V, GND) motion detector.
When detector triggers, I need to send signal (distance at least 5km) to another Arduino Nano and catch it. As far as I understand, 433Mhz is the optimal frequency for this.
Please suggest me what should I use? Which circuit, protocol etc. The solution should be as simple and as cheap as possible
Thank you in advance!
Well LoRa will go up to 10 times further than most all other radio types.
However, which RF devices will work, depends entirely on where the 5-10km is, if there is very clear line of sight between transmitter and receiver then there is quite a few RF devices that will cover the distance.
So describe the actual location, heights of antennas, whether its flat of hilly, what obstructs the path, if its line of sight etc for a better answer.
Thank you for the reply! It's on town outskirts, directed to another town outskirts. Not always with clear line of sight, because there are trees, little hills etc. There are other devices in this region, so there may be some few interferences too. About height of antennas I'm not sure.
I'ver read about LoRa and I think thats what I need. Can you please suggest some particular module that can fit? Maybe one of more powerful ones
Not good
Although LoRa has been tested up to 832km, that was with clear line of sight, ground to high altitude balloon.
If there are hills in the way, forget it.
By all means buy a couple of modules, the RFM95s are as good as any, and do a range test.
Legal restrictions will often prevent you using higher powers or fancy antennas.
433MHz is a frequency with lot of users. Doorbells, weather stations, key fob, .... => lot of interferences.
GSM modem and MQTT.
Is there wi-fi & internet connection in both locations?
It won't work in the cross-town situation you described.
The Internet and cell phones (or regular wired phones) can go around the world!!! 
Of course you do need access to a connection or cell tower.
In most countries the radio spectrum is highly regulated and you can't just build or set-up a high power transmitter.
Companies sometimes use microwave dishes between locations but of course that's expensive and requires professional installation and I assume some kind of permit or license.
Can you put up antennas on both sides, high enough to go over the trees and hills? In that case RF should work...
Hello juneor
Take some time an visit a local radio amateur club and ask for some solutions.
Dont quite see how the Amateur radio sphere would be much help.
For Amateur radio if you want a signal to go further then you can use more power and\or better antennas. However even if you have a ham license, in a lot of places the license can only be used for messages between hams, you cannot do general domestic sensor stuff.
In the unlicensed ISM bands, host devices are mostly already operating at the maximum ERP so increasing TX power or using better antennas is not legal.
There are a few places in the World where larger amounts of power than the standard 10mW @ 434Mhz are allowed, but we dont know where the OP is based.
Don't tell us what doesn't work, it won't help us!
And if you never don't ask, you will never get an answer.
IF this is truly your project, then you need a transmitter at one end and a receiver at the other end. ALL the hobby modules for Arduino seem to be transcievers, Meaning they transmit and they also receive.
As pointed out, the transmit power and antenna are limited. BUT the receive antenna can be as big as you want and can even use separate low noise preamplifiers to increase the range of the receiver.
So that comes down to what you want. A hobby transceiver or a one-way only setup?
That is indeed true, higher gain receive antrennas are good, but then not cheap to buy or are easy to setup.
As for LNAs, they would improve the range of the short range RF devices (non LoRa) but even then you would need an (very) expensive LNAL to get even close to the range that LoRa devices would provide, without the LNA.
You will only transmit through a LNA just one time!
Indeed, almost certainly, not legal.
And of course how can you tell which or how many essential services you could destroy ?
So why even suggest it ?
FYI, if the FCC finds out about an illegal signal, depending on where it is and what the collateral damage it could cause they dispatch a triangulation team of specially equipped vans and pinpoint it in a matter of minutes and since FCC is FEDERAL, it
would most likely be the FBI knocking down your door. The operative phrase here is " finds out about". If it's far enough from any city radio signals or an airport it would go to the bottom of the cue and if they do show up it could be months, since there is no benefit to tracking down signals that don't interfere with anything important.
FCC
You likely are not aware but the Arduino forum is a popular site for terrorists seeking technical advise for sending detonator signals and other nefarious things. In one case Homeland Security contacted me about a link I sent for a forum post in this topic where a guy wanted to know how to build an EMP device that would take out several city blocks. They didn't have to take my word for it because they could read the post themselves. It did take them a couple of months to call though but they were all over it. How do we know you aren't one of the bad guys trying to do something like that ?
For my sake, I fully understand the complications using illegal radio equipment, both technical and legal actions. However, this is a international forum and FCC is not present in other countrys. With regards of terrorists, I have that in mind and I do not like to give technical advice that might damage or destroy humans. So, for that reason, I do not share some of hardware or drone projects, that would "open the mind" for crazy people. I delete my post, related to this topic.
All countrys has institute to regulated the ether using. In Belgium is that BIPT. With 3 cars they find a transmitter with accuracy of meters. They where offen used the time the 27MHz band wasn't licensed.
For VHF use I have done my exams by BIPT. To use VHF transmitter/receiver there must be pay duty.
There was one forum post where the poster was requesting details how to 'trigger' something 3km away. As you can imagine, that was a red flag.
When confronted with the nefarious potential of his request, he deleted is post amd was never heard from again. No idea what country he was in.