hall current sensor potential failure mode
You specify AC mains operation and a 5A sensor.
This answer focuses mainly (but not solely) on the consequences of the internal shunt in the sensor IC failing open circuit (as can happen).   

My discussion below assumes potential fault currents far in excess of 5A, or indeed, in excess of the continuous 65A rated current of the ACS723. I've also mentioned DC sensing operation. AC sensing is somewhat less design demanding than DC due to the greater likelihood that an arc will extinguish.   

In many mains based applications limiting currents to below eg 65A under short circuit is 'easy enough'. However, if current limiting is not specifically designed in, AC mains will often happily source many many hundreds of amps under short circuit. The duration of such overcurrent events may be short - but not always short enough.

I'll deal only with the ACS723 as the 712 has an inferior specification and is obsolete. Anything that applies to the 723 will apply to the 712, but more so. 

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The ACS723 is rated at 65A continuous and claims 0.65 milliohm shunt resistance.
At 65A dissipation = I^2.R = 2.75 Watt.  

Thermal resistance is 5 C/W when mounted in their development board or 23 C/W junction to air bare.  At say 3 Watt dissipation (add solder joints,...) temperature rise above ambient would be about 15 degrees c and 115 c respectively. Tjmax is specified at 165 c. That allows (just) operation in 50 c free air with no heatsinking - so quite modest heatsinking will usually keep it "cool enough". Cooler is better for long life but under those conditions no major short term failures should be expected.

If you use it in a system with a battery capable of providing hundreds of amps (as I have done) or with AC mains and a good current path, and then experience a short circuit somewhere "downstream" of the sensor (as I have done) then things rapidly can get 'not so good'.    

At say 200A the dissipation rises to 26 Watts - the evaluation board heatsinking will keep the temperature in check for a very short while - but 26W is too much for any normal PCB copper based heatsinking. At 300A, it's toast. 

At somewhere above 65A and quite possibly well below 200A the internal shunt may fuse. Unless they have designed an HRC fuse into the package (and they haven't) then under DC an impressive arc will form and sustain until interrupted elsewhere. With AC it MAY not form a sustaining arc, but probably will. 

Once an arc forms, all bets are off.
Ask me how I know :-).  

The package will carbonise, the PCBA (unless super super special) will join in the fun and a small fire will probably start.  Worst case, and quite probably, energy from the current monitored circuit will enter the now-no-way-isolated low voltage power supply and control circuits. Results will depend on design, protection against such an event and Murphy.

To prevent the above you can


limit Imax to 65A in some way
fuse the circuit to open the fuse below 65A.
A fast blow fuse is required as you don't know how fast the IC shunt fuses, and you MUST prevent it doing so. 
Prevent more than 65A flowing in the shunt in some manner during higher current faults. This is a less likely approach but could be achieved with eg a fast acting electronic bypass. 


Placing the low voltage side of the sensor in an isolated node with 'communications' and powering via fail-safe interfaces is certainly possible and may be viable. But 


In situations where high fault currents cannot be designed out I'd expect high current side HRC fusing to be a reasonably good solution.   
In situations where 5A max load was desired and significant power loss in feed circuits was acceptable then ensuring adequate resistance (or inductance with AC) is present is probably satisfactory.  eg at 230 VAC, to limit I to 65A max R = V/I = 300Vpk/65 ~~~= 5 ohms. At 5A the loss in 5 ohms is P = I^2R =  125 Watts! This is a significant dissipation level -  an HRC fuse and more modest resistance levels are probably in order. 


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HRC Fuses!:

I mentioned HRC (High Rupture Capacity) fuses several times above.
The need for such fuses when arcs can form is crucial. A fuse which opens at say 20A but which can sustain an arc of hundreds of amps (which many non HRC fuses can) is worse than useless as it provides a degree of confidence which is wholly without foundation.