Installing a Hard Disk Drive from an old desktop into a Dell Inspiron and/or Dell Vostro?

Yes, it can.  It's a  standard SATA drive.

You will not be able to boot it - nor run the existing Windows from it though - it can be used for storage, however,

The drive is a standard SATA desktop model - it will fit the newer system.

it can be used for storage, however,

Thank you!

It is my intention to transfer the files from the Seagate Barracuda 7200.7 Hard Disk Drive of the broken Dell Dimension 5000 to the new desktop and use the 'old' HDD as an internal back-up drive.

I was somewhat confused, because installing a Hard Disk Drive is a little bit different on a Dell Dimension 5000. See: Installing a Hard Drive.

Yes, it can.  It's a  standard SATA drive. You will not be able to boot it - nor run the existing Windows from it though - it can be used for storage, however,

An XP "Repair Install" would allow it to boot, as would a clean install.

[quote user="ejn63"] You will not be able to boot it - nor run the existing Windows from it though - it can be used for storage, however,

An XP "Repair Install" would allow it to boot, as would a clean install.[/quote]

Can't I boot by doing the follwing?:

1) Replace the new HDD of the Dell Vostro/Dell Inspiron with the 'old' HDD of the Dell Dimension

2) Boot (running Windows XP)

3) Add the 'new' HDD of the Dell Vostro/Dell Inspiron as a secondary Hard Disk Drive

4) Transfer all the data from the 'old' HDD of the Dell Dimension to the secondary Hard Disk Drive

5) Remove the Primary Hard-Drive ("'old' HDD of the Dell Dimension")

6) Boot again (running Windows 7/Windows 8)

7) Format the 'old' HDD of the Dell Dimension

8) Back-up the data

It's unlikely you'd be able to boot from the old drive without a repair install first.

When you Move a hard drive to a new machine you get (Stop 0x0000007b) inaccessible boot device