My assumptions:
5 days (nights)
7 hours of CPAP per night
Your pressure is about 10 or 11 cmh2o
Your CPAP or APAP will be directly powered from a 12 volt battery
No humidifier.
5 days x 7 hours x 1 Amp hour = 35 Ah
This number will have to be adjusted if your pressure is significantly above or below 10 cmh2o
You have three choices for a battery: Li-ion battery $$$, gelled electrolyte $, or AGM $.
Li-ion batteries are found in Battery Geek CPAP batteries, gelled electrolyte batteries are found in portable car batteries, and AGM batteries are large, heavy, spill proof deep cell batteries similar to car batteries.
As you will be packing the battery, you will want the lightest battery that will power your CPAP, which will be Li-ion. There are some more esoteric batteries that might be lighter, but they are not readily available in a form that is suitable for our needs.
So, what you are looking for is a light-weight CPAP machine that can be powered directly from a 12 Volt battery, a Li-ion battery that will provide at least 35 Ah, and a power cord to connect your battery to your CPAP machine. If weight were not an issue, an AGM would be much cheaper
There may be other sources for suitable 12 volt Li-ion packs, but the one I use is a Battery Geek BG-C222, which is 18 AH -- about half of what you need. My BG-C222 weights 3.5 lbs and will power my CPAP for almost three days, so this indicates that the 35 Ah calculation is reasonable. Battery Geek also makes a BG-C444 battery, which weighs 9 pounds and is about twice the capacity of the BG-C222; it should power a CPAP for 35 hours. The down side to these batteries is that they are expensive: The BG-C222 lists for $435 and the BG-C44 lists for $795; they can be found at a cheaper price. The BG-C222 can be carried onto an airplane in a carry-on and the BG-C444 would have to be put into checked luggage.
There are several lightweight CPAPs that can be powered directly from a battery, my favorite is the IntelliPAP. Most Online CPAP stores sell the proper cable, and the BG-C222 includes the proper cable (I think that the BG-C444 also includes the CPAP cable). You will also need a battery charger suitable for the battery. The Battery Geek batteries include an AC powered charger. Solar power chargers are probably impractical for your use; they are large, the supporting electronics are heavy, they are even more expensive, and they require exposure to full sun for many hours every day..
The BG-C222
The BG-C444