How long does the District Attorney in New York State have to indict someone after arrest is made for a class C felony?

The generl rule is that prosecution for a felony must be commenced  within 5 years of the commission of the crime or within 6 months of the commencement of the case, the prosecutor must be ready for trial. There are many exclusions of time for example if the defendant makes a motion, that time is not held against the prosecution.