This is not an answer, but here's some info that might help you:
"5V panel" does not mean that the output from the panel will always be five volts. The current that a panel can produce from a given amount of light is limited, and the more current the external circuit draws from the panel, the more the voltage will drop. The voltage varies only by a few percent over most of the current range, but as the current gets close to the maximum, the voltage suddenly plummets toward zero.
The operating point where the slope of the voltage/current relationship suddenly changes is called the Maximum Power Point. That's where the panel is operating most efficiently. Smart solar battery chargers will use a "Maximum Power Point Tracking" (MPPT) algorithm that continually adjusts the battery charging rate so as to keep the panel operating at the maximum power point.
When they tell you the "voltage" of a big solar panel, they're usually telling you the voltage of the maximum power point when the panel is directly facing the sun and the sun is high in a clear, cloudless sky. That voltage is often designated as \$V_{mp}\$. I don't know if there is any reporting convention for a little panel like the one that you're using. "5V" could be \$V_{mp}\$, or it could be the open circuit voltage, \$V_{oc}\$.
The open circuit voltage sounds better in advertisements because it's around 20% higher than \$V_{mp}\$, but it's misleading because "open circuit" means no current is flowing, No power is being generated.
https://en.wikipedia.org/wiki/Maximum_power_point_tracking
https://www.victronenergy.com/blog/2020/02/20/pv-panel-output-voltage-shadow-effect/
It doesn’t make sense to me to supply 3.7 V to a 5 V pump
It might or it might not make sense. If the pump's motor is a simple, brushed DC motor, then 5V probably is the maximum allowed voltage. A brushed DC motor will spin at a speed that is approximately proportional to the applied voltage. If you apply 3.7V to a "5V" motor, then the motor will spin at around 74% of the maximum allowed speed.
On the other hand, if the pump has a fancy, brushless DC motor (a.k.a., "BLDC motor") then the motor's built-in electronic controller probably will not work at all if you don't supply the expected voltage.