HP Officejet 5610 All-in-One Printer

Unfortunately, not all USB printers are compatible with AirPort base stations. In addition, the AirPort's USB port does not support the "advanced" printer functions, like scanning, copying or faxing, of multi-function printers.

To see if your printer is compatible, take a look at one of these iFelix Unofficial AirPort Printer Compatibility links, depending on which AirPort base station you have:
o 802.11g AirPort Extreme Base Station (AEBS) or AirPort Express Base Station (AX)
o 802.11n AirPort Extreme Base Station (AEBSn)

If your printer isn't listed, it doesn't necessarily mean it won't work, but simply that it has not been verified. iFelix also provides the following workaround for printers not on the list that would certainly be worth a try.

Also you can try these Tech Support articles to see if it will help:
o Printer troubleshooting for AirPort Extreme and AirPort Express
o HP All-in-One, Photosmart and Deskjet Products - Mac OS: Connecting to USB Port of Wireless Routers