Sprint is different from other carriers in that the sim (ICCID) and phone (IMEI) are "married" and one cannot simply swap sims between phones as one can with Verizon or GSM carriers.
You need the sim card your mother used in that phone.
You can change sims on Sprint phones but you must deactivate the phone and sim first. It is very rare that this is necessary. The phone and sim should stay together.
If you do not have the sim from your mother's phone, you need to contact the carrier and have the new sim activated for you. Should you be able to access device swap online you can do the swap yourself if you have a placeholder ESN.
The model 5c takes one of three sim models: SIMGLW436C, SIMOLW416C, and SIMOLW506C