Powering 5V LED strips using 12V
If I understood you correctly you basically want to put an LM1084 every around 13m/5=2.6m, so each one of them will need to supply a current of 2.6m*1.8A/m = 4.7A (I just took your numbers, I didn't check if they are correct).

The thing with the LDOs, like the LM1084, is that you have to be very careful regarding the maximum power dissipation they can afford due to their low efficiency. The reason is that simply the excess power that is not needed on each of them will be turned to heat. That is equal to \$(Vin-Vout)*Iout = (12V-5V)*4.7A = 32.9W\$! All this power will be turned to heat, which is enormous!

Check the chapter 10.3 ("Thermal considerations") of the datasheet on this very important issue.

Basically you have to find out if this 33W of heat can be dissipated in the package. If not, consider using a heat sink. If even with the heat sink the dissipation is still too high, you'll have to find and use a switching regulator instead, where the efficiencies achieved are usually around 80% to 90%.

UPDATE:
Of course another thing is that your input power supply, the 12V/10A will not be able to provide enough current! The LDOs need (almost) so much current at their input as they provide at their output, meaning the 5 LM1084 will need a total current equal to 5*4.7A=23.5A, which is higher than the 10A of your power source.