Are you planning on driving a rental car each day, jeff? For our early April trip a few years ago, we did a mix. We were there longer then 5 days, though. The days we had a rental car, we did day trips out of Reykjavik, returning for each night, although 2 days were in Reykjavik itself, no car.
Our excursion outside of Reykjavik was actually on a tour with Icelandic Adventure Guides, which traveled the south coast, as far east as Jokulsarlon, then back to Reykjavik over a few days. There we stayed in a different place each night. Early spring was too extreme to visit far north. I’d imagine October could be a similar climate, and with just 5 days, I wouldn’t imagine you’d be going too far over those 5 days to reach many, many separate locations for single stays.