Can I upgrade from one to the next? I have a Dell Studio XPS and I am unsure about power/size constraints.
The HD 5450 is an entry-level card intended for HTPC applications and draws very little power, at 19.1 watts (source). The HD 5970 is a top-of-the-line dual-GPU video card and requires as much as 294 watts to operate (source). You will need a PSU with one 8-pin and one 6-pin PCI Express power connector, and it needs to be able to supply at least 650 watts (source). As systems of the type you mentioned generally do not have an adequate power supply (OEM power supplies are often inadequate for major upgrades, except for expensive high-end gaming systems), you will probably need to upgrade the power supply. You may want to consider any one of the modular Corsair PSUs listed here on the Corsair website.
You can probably make the upgrade, but you will need to replace the stock power supply.