Can I run my hp 5610office jet all in one printer on vista home premium ?

That's not a Windows Update but HP Update

Yes
You can download the HP printer drivers from their supportWEB site. Please click on this link and
select your model printer to download:- http://welcome.hp.com/country/us/en/support.html

HP Print Diagnostic Utility was created to help users troubleshoot and correct many common problems on Windows-based computers that can prevent printing.Follow the on-screen instructions to run the utility.

Details and specifications

File name:HPPDU.exe [1/1, 1.54M]System requirements:No additional prerequisitesReleased:2010-08-13Version:3.0.0.013Compatibility:Microsoft Windows Vista, Microsoft Windows Vista Home Premium (32-bit), Microsoft Windows Vista Home Basic (32-bit), Microsoft Windows Vista Business (32-bit), Microsoft Windows Vista Ultimate (32-bit), Microsoft Windows 7 (32-bit), Microsoft Windows 7 Home Basic (32-bit), Microsoft Windows 7 Home Premium (32-bit), Microsoft Windows 7 Professional (32-bit), Microsoft Windows 7 Enterprise (32-bit), Microsoft Windows 7 Ultimate (32-bit), Microsoft Windows 7 Home Basic (64-bit), Microsoft Windows 7 Home Premium (64-bit), Microsoft Windows 7 Professional (64-bit), Microsoft Windows 7 Enterprise (64-bit), Microsoft Windows 7 Ultimate (64-bit), Microsoft Windows 7 (64-bit), Microsoft Windows Vista (64-bit), Microsoft Windows Vista Home Basic (64-bit), Microsoft Windows Vista Home Premium (64-bit), Microsoft Windows Vista Business (64-bit), Microsoft Windows Vista Enterprise (64-bit), Microsoft Windows Vista Enterprise (32-bit), Microsoft Windows XPFix/Enhancement:This version of the HP Print Diagnostic Utility provides an improved user interface in multiple languages, improved diagnostic and problem resolution capability, and support for usb and network connected devices.

TRY HP Print Diagnostic Utility was created to help users troubleshoot and correct many common problems on Windows-based computers that can prevent printing.Follow the on-screen instructions to run the utility. Details and specifications File name: HPPDU.exe [1/1, 1.54M] System requirements: No additional prerequisites Released: 2010-08-13 Version: 3.0.0.013 Compatibility: Microsoft Windows Vista, Microsoft Windows Vista Home Premium (32-bit), Microsoft Windows Vista Home Basic (32-bit), Microsoft Windows Vista Business (32-bit), Microsoft Windows Vista Ultimate (32-bit), Microsoft Windows 7 (32-bit), Microsoft Windows 7 Home Basic (32-bit), Microsoft Windows 7 Home Premium (32-bit), Microsoft Windows 7 Professional (32-bit), Microsoft Windows 7 Enterprise (32-bit), Microsoft Windows 7 Ultimate (32-bit), Microsoft Windows 7 Home Basic (64-bit), Microsoft Windows 7 Home Premium (64-bit), Microsoft Windows 7 Professional (64-bit), Microsoft Windows 7 Enterprise (64-bit), Microsoft Windows 7 Ultimate (64-bit), Microsoft Windows 7 (64-bit), Microsoft Windows Vista (64-bit), Microsoft Windows Vista Home Basic (64-bit), Microsoft Windows Vista Home Premium (64-bit), Microsoft Windows Vista Business (64-bit), Microsoft Windows Vista Enterprise (64-bit), Microsoft Windows Vista Enterprise (32-bit), Microsoft Windows XP Fix/Enhancement: This version of the HP Print Diagnostic Utility provides an improved user interface in multiple languages, improved diagnostic and problem resolution capability, and support for usb and network connected devices.

HP Print Diagnostic Utility was created to help users troubleshoot and correct many common problems on Windows-based computers that can prevent printing.Follow the on-screen instructions to run the utility. Details and specifications File name: HPPDU.exe [1/1, 1.54M] System requirements: No additional prerequisites Released: 2010-08-13 Version: 3.0.0.013 Compatibility: Microsoft Windows Vista, Microsoft Windows Vista Home Premium (32-bit), Microsoft Windows Vista Home Basic (32-bit), Microsoft Windows Vista Business (32-bit), Microsoft Windows Vista Ultimate (32-bit), Microsoft Windows 7 (32-bit), Microsoft Windows 7 Home Basic (32-bit), Microsoft Windows 7 Home Premium (32-bit), Microsoft Windows 7 Professional (32-bit), Microsoft Windows 7 Enterprise (32-bit), Microsoft Windows 7 Ultimate (32-bit), Microsoft Windows 7 Home Basic (64-bit), Microsoft Windows 7 Home Premium (64-bit), Microsoft Windows 7 Professional (64-bit), Microsoft Windows 7 Enterprise (64-bit), Microsoft Windows 7 Ultimate (64-bit), Microsoft Windows 7 (64-bit), Microsoft Windows Vista (64-bit), Microsoft Windows Vista Home Basic (64-bit), Microsoft Windows Vista Home Premium (64-bit), Microsoft Windows Vista Business (64-bit), Microsoft Windows Vista Enterprise (64-bit), Microsoft Windows Vista Enterprise (32-bit), Microsoft Windows XP Fix/Enhancement: This version of the HP Print Diagnostic Utility provides an improved user interface in multiple languages, improved diagnostic and problem resolution capability, and support for usb and network connected devices.

HP Print Diagnostic Utility was created to help users troubleshoot and correct many common problems on Windows-based computers that can prevent printing.Follow the on-screen instructions to run the utility. Details and specifications File name: HPPDU.exe [1/1, 1.54M] System requirements: No additional prerequisites Released: 2010-08-13 Version: 3.0.0.013 Compatibility: Microsoft Windows Vista, Microsoft Windows Vista Home Premium (32-bit), Microsoft Windows Vista Home Basic (32-bit), Microsoft Windows Vista Business (32-bit), Microsoft Windows Vista Ultimate (32-bit), Microsoft Windows 7 (32-bit), Microsoft Windows 7 Home Basic (32-bit), Microsoft Windows 7 Home Premium (32-bit), Microsoft Windows 7 Professional (32-bit), Microsoft Windows 7 Enterprise (32-bit), Microsoft Windows 7 Ultimate (32-bit), Microsoft Windows 7 Home Basic (64-bit), Microsoft Windows 7 Home Premium (64-bit), Microsoft Windows 7 Professional (64-bit), Microsoft Windows 7 Enterprise (64-bit), Microsoft Windows 7 Ultimate (64-bit), Microsoft Windows 7 (64-bit), Microsoft Windows Vista (64-bit), Microsoft Windows Vista Home Basic (64-bit), Microsoft Windows Vista Home Premium (64-bit), Microsoft Windows Vista Business (64-bit), Microsoft Windows Vista Enterprise (64-bit), Microsoft Windows Vista Enterprise (32-bit), Microsoft Windows XP Fix/Enhancement: This version of the HP Print Diagnostic Utility provides an improved user interface in multiple languages, improved diagnostic and problem resolution capability, and support for usb and network connected devices.

hi
well you must go to the device manager through start->run->devemgmt.msc and there you can check the status of your of printer.If it shows the connection then you must go to the printer option in control panel and check the connect the computer.If still it doesnt work then you can visit our site where our expert can help u.OUR url is----------http://robs-tech.blogspot.com/2009/06/free-technical-support-regarding.html

http://h20000.www2.hp.com/bizsupport/TechSupport/DriverDownload.jsp?prodNameId=1140780&lang=en&cc=us&prodTypeId=18972&prodSeriesId=1161389&taskId=135

Go there and try download the Drivers and Utility for the 64-bit Version of Vista. Pretty bad that HP's own website has the info you need, yet they say it won't work.

for wireless communication you must have wiress terminals to both end. then instll drivers.
that is all to do.

good day

first of all instal this fix:
http://support.microsoft.com/default.aspx?scid=kb%3ben-us%3b936003

and 2-nd be sure the driver is for vista not for xp

tell me if this works