A DFA is possible I guess which is interesting, see if the following
DFA works, since the existence of the DFA relates to the existence of
a Regular Expression Describing the language

State/Input         0                    1
q00                  q10                 q01
q10                  q20                 q11
q20                  q30                 q21
q30                  q40                 q31
q40                  q00                 q41

q01                  q11                 q00
q11                  q21                 q10
q21                  q31                 q20
q31                  q41                 q30
q41                  q01                 q40

The final state is q00.

In this DFA the first subscript denotes the number of zeros % 5 and
the second describes the number of ones % 2

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