If you want to combine the number five, because that is the day you were given the cat, and its female sex, you can use the ordinal number which, unlike the cardinal one, varies according to gender:
Mi gata se llama "Quinta" porque me la regalaron el quinto día de mayo.
Spanish names are usually O for boys and A for girls. Juan/Juana.
There are a few exceptions as posted by wimi above.
However, numbers in Spanish are invariable so cinca is not the "feminine of cinco".
Uno, dos, tres, cuatro, cinco, seis= Invariable.
Cinca is merely attempting to make feminine something that is invariable.
You can name your cat ...
If you are asking whether there are masculine names that end in "a" and feminine names that end in "o", then there are. For example:
Borja and Bautista are masculine names ending in "a"
Consuelo and Amparo are feminine names ending in "o".
So calling a female cat "Cinco" would not violate any rule. No rule ...