Is it possible to connect Li-Ion Batteries in series?
You would not be connecting two Li-ion batteries in series.  Li-ion batteries have a 3.6V output not 5V.

Whether they are in series is less of an issue than the current draw. You should be fine as long as you do not discharge the batteries too fast. That should not be an issue because li-ion batteries are very regulated, must pass safety standard tests, and there is likely a current limit on the output.

Many inexpensive off brand li-ion battery packs are not li-ion but NiMH. If the battery packs were shipped UPS, FedEx, or any way other than strictly ground, they are likely not Li-ion.  UPS and FedEx will not ship Li-ion batteries or battery packs unless they are packaged with a device that uses the batteries.