I have a Photosmart 5510d series (751669) printer at my cottage with a wireless connection there. Is this printer strictly wireless or can I connect it using a USB?
Yes, you can connect the printer using the USB port. In fact, all of the 5510 printer series have the USB ready for connection.
You can check all the specifications using the following URL: http://support.hp.com/us-en/product/HP-Photosmart-5510-e-All-in-One-Printer-series---B111/5053904/model/5053905/document/c02907978/
However, USB connection requires a driver that can be downloaded from the same page: http://support.hp.com/us-en/drivers/selfservice/HP-Photosmart-5510-e-All-in-One-Printer-series---B111/5053904/model/5053905