I won't be able to tell you which solar panel or battery to use, but I can tell you how to figure that out.
For the battery there are a few different ways to figure this out:
- The most common way to do this at the professional level is to build the device and run it attached to an energy meter and measure it for an hour or two performing its usage, and use that to calculate how much it will use over a 48 hour period. That being said that type of test equipment is not really a hobbyist piece of equipment and probably not something you are wanting to obtain for this project.
- You can try and use the datasheets for all of your components to determine their idle and active current draw is, add them up for idle and active, adjust the values based upon the efficiency of your step up converter (so if it only 75% efficient, divide them by .75), guesstimate how long your sensor read process will take, multiply your active current draw times the voltage and times the time it will take (in hours, so if this is a few seconds, it will be a really small decimal), multiply your idle current draw times the voltage and times .083 hours (5 minutes), add those two together multiply it times 12 (12 - 5 minute periods per hour) and then by 48 (two days) and that will be an estimate of your energy usage for two days. Now this will be a very rough estimate as the datasheets only provide nominal values, and their actual usage in practice may be different, which leads me to the final option...
- A hybrid between the two above solutions. Set up your device and have it read the sensors and transmit continuously. Then use a multi-meter to measure the current usage of it actively being used. Repeat the measurement again but this time with it running on an indefinite timer to simulate being idle. Then take those two numbers and use the above formula substituting the datasheet estimates with your actual measurements to get a much more accurate picture of what your energy usage will be.
Once you have your energy usage (this will be in milli-Watt-Hours or mWH) pick a battery voltage you will be using (this is based on the charge circuit you are using, typically, single cell lithium ion batteries are 3.7 or 4.2, with multi-cell batteries being multiples of those), divide your energy by the voltage to get the power (in milli-Amp-Hours or mAH) and you'll want to pick a battery greater than that. You'll also want to double check the data sheet of your step up converter and see what the drop out voltage is, and then compare that to the datasheet for the battery and see at what capacity it hits that voltage. You'll want to make sure that it is at least 80%. Otherwise you'll have to pick a different battery with a larger capacity, or a different step up converter with a lower dropout voltage.
For the solar panel, what you will want to do is get a battery charger designed specifically for use with solar panels. This is because when it says 5.5v solar panel, that is it's nominal voltage in full sunlight, however, it most often will not be that and will vary greatly throughout the day. What this means is that solar panels are basically on unregulated power supply, and most battery chargers require a regulated power source. With a solar specific batter charger, it is designed such that it can handle voltage variation and sudden dropouts. Usually these chargers come with a recommendation as far as voltage and current requirements and those specifications should form the basis of your solar panel selection.
So for example, if you have a battery, on the datasheet it will list what its charge current is, and you'll want to make sure you have a charger circuit that can supply that amount of current. Then you'll want to take a look at the datasheet for the charger circuit, see what current it requires and then make sure that the solar panel can provide that current.