Five generations back is a bit borderline for detecting DNA from one specific ancestor, but it's possible an autosomal test would pick it up.
Right now I would recommend 23andMe for their Ancestry Composition report. If it doesn't pan out, your results will still be interesting for other purposes (e.g. finding cousins).
If you have older generations available for testing, they are more likely to retain some DNA from the ancestor(s) in question, so you might want to find some candidates from both your maternal and paternal sides.