Hi,
if we send a 5 digit number from computer and they are not read by the host microcontroller same time.
You need to read the microcontroller datasheet about hardware UART buffer.
But you are free to install a software buffer in your microcontroller.
Decades of years we trusted in UART. And in the industry it is still alive.
MODBUS, Profibus and so on can be implemented with UART.
But UART is just the serializer and deserializer.
* Additionally you have a hardware interface (RS232, RS485, RF, optical...)
* and you have a protocol. Use the correct protocol to detect errors and - if you like - to re transmit the bad block of data.
* and for sure you need to use the correct cables, too.
* .. and the correct baud rate...
Indeed I´d say UART is not the problem. I think it´s rather external EMI error sources, cabling, interface, software...
Klaus