What's the term for this type of battery?
That battery is a pouch lithium-ion battery.
If he green board contains charging and (very likely and hopefully) protection circuitry, it will be slightly specific to the speed at which the battery can be charged, and how much current the attached circuit wants to draw.
Whether it contains that circuitry depends on how we need to interpret your &quot;charged with 5V&quot; statement: if you mean that the device that this battery was part of is connected to 5V for charging, then most likely, the charging circuitry is elsewhere and this is just lithium battery, and the green board mostly serves connection/soldering purposes.
If you meant that 5V can be directly attached to the leads on this battery for charging, then there needs to be a non-negligible amount of electronics on the backside of the green board, which will manage charging/discharging.
Since there's no markings on the battery, it's impossible to tell you the former capacity of the battery, sadly, or maximum discharge currents.