I missed the post the other day and have been working and not online. Remind me what wattage heating element you have?
As to the PID breaker, 5 amps is a little large. For the PID I would recommend a fast blow 1 amp fuse because they trip much faster than a thermal breaker would.
As to the heating element there are two schools of thought. Need it or don't?
You probably don't need one. Reason is the wire to the element (which is usually in the neighborhood of 1,500 watts) is generally rated for the same amp capacity as the home wire to the smoker. The purpose of a breaker or fuse is to protect the device, in this case a heating element, but in other cases the "device" can also be a wire that is of a smaller gauge or amperage capacity than the household wire to the outlet. Since in your case they will be roughly the same capacity, the breaker that protects the wire in the house would be properly rated to protect the element and the larger wiring in the smoker (usually 14 to 12 gauge). If your outlet the smoker is plugged in to is on a 15 amp breaker in your main panel, then adding a 2nd 15 amp push button breaker at the smoker for the element and/or main power, does not add any protection at all. It will not hurt, but it probably will not help either.
However 99% of the builds use a smaller gauge wire branching off to provide power to the PID inside the smoker electronics box, as the PID is a very low amp draw device. Also the PID is much more sensitive internally to a electrical problem than the element is, so it has different protection needs. Hence the recommendation of a 1 amp "fast blow" fuse (not a breaker) to protect the power line going from the terminal strip to the PID only. A push button breaker is usually a thermal device. It will trip before the wire is damaged if it is sized correctly (depends on your wire gauge as the the value here), but the PID is much more sensitive to damage than the wire so the 1 amp fast blow recommendation is to protect the PID not the wire (and being lower than the wire rating would also protect the wire with a huge margin of safety - fuses & breakers should be sized for the lowest amp rated part of the branch which in this case is the PID). You can still damage a PID's electronics even if it's fused properly. The fuse is just the best bet on providing some level of protection. Remember the fuse is protecting the components from catastrophic disaster which would usually start a fire or make a metal component of the smoker cabinet electrified and deadly if touched. It "may" keep the sensitive electronics inside the PID from frying. Some brands/models are more sensitive to quick damage than others due to the internal construction.
You can put the fuse in either of the two wires providing power to the PID, but the "by the book" method would be to the side that is electrically connected back to the black wire from the household wiring. Same is true for the 15 amp breaker if you decide to use it.
Connections for the smaller fuse/breaker would either be via a solder terminal or a spade lug but I have seen fuse holders with screw terminals. I would go with solder myself, but there is nothing wrong with a properly applied spade (flat bladed crimp on type female connector that friction fits on a male flat terminal on the fuse body). A 15 amp unit will usually have screw terminals.
Does this help?