Here is the manual install method I recommend. This will NOT use the ATI Install Manager method, which doesn't seem to be working for you. No problem... you can (or hopefully SHOULD be able to) install the updated drivers manually.
But please follow the steps below, and then report back as to whether or not this works for you.
(1) Download the 11.3 Catalyst drivers for ATI Mobility products from this location. Actually, that file is the large 86MB "suite" installer file that includes device driver, Catalyst Control Center, and OCL.
We're not going to actually run this file (which is really the ATI Install Manager in charge of things) to completion. But you will RUN it just far enough to self-expand itself into a \Support folder location on your computer somewhere (say, in C:\ATI by default) so that we can navigate to it later.
(2) RUN that 86.4MB downloaded file yourself, through the first step which is the self-expansion somewhere. You can either accept the default target location for the self-expanded output folder or modify it as you see fit. When you're ready, push the INSTALL button and it will self-expand.
(3) Eventually, after self-expanding it will auto-execute the SETUP.EXE program inside (i.e. the ATI Catalyst Install Manager) and will reach the initial "Welcome" presentation.
(4) Push the CANCEL button in the lower right corner. We don't want to run this ATI Installer because it doesn't seem to be working for you. At the very least, it's not part of the "manual driver update" procedure we're going through.
Note that this same manual driver upgrade procedure is very much what actually happens when a hardware vendor makes new drivers available to Microsoft for delivery through Windows Update, and you choose to let Windows Update apply that driver upgrade. Win7's Device Manager gets involved and applies the new driver files very much like we're doing it now, except quietly and under the covers.
Anyway, after you push that CANCEL button you will now have all of the driver file components for 11.3 Catalyst for the Mobility products... in a folder structure under \Support.
In that same folder location you also have the installation files for Catalyst Media Center (if you want to run that one later) and OCL, but first let's get the driver installed.
(5) Now on your desktop (or from the Start button) right-click on the Computer object, select Properties from the popup menu, select Device Manager, and click on the "expand" arrow next to "Display adapters" on Device Manager's presentation to reveal your currently installed ATI Radeon Mobility HD 5470.
Now right-click on that Mobility HD 5470 item to get a popup menu. DO NOT CLICK ON PROPERTIES in that menu... but DO CLICK ON "update driver software" to enter the manual driver upgrade dialog.
For example, on my own desktop with an HD 4850 video card:
(6) When you select "update driver software" you will then get a new window with the "how do you want to search for driver software?" question, and you will click on the SECOND one... "browse my computer for driver software, locate and install driver software MANUALLY".
(7) This will then present another window, to allow you to navigate to where the driver software files are located (i.e. that \Support folder from the self-expansion first step).
The "browse" button on this dialog really doesn't work as you'd expect (at least it doesn't for me), but you can just force the auto-fill process to automatically fill in the location for you, by clearing the area and then manually typing in the starting high-level folder location.
For example, start with "C:\ATI". Then, if you just type one more character of "\" in the next position (to indicate to auto-fill the end of the prior path level and the start of the next path level), auto-fill will look at the choices available and present them all to you. You then just select which one you want to move to next, and it will continue.
But really, it's not necessary to fully complete the target name where the INF drivers live. In fact, it's really not necessary to go much lower than C:\ATI\Support (or whatever high-level location you allowed the self-expansion of that 86.4MB file to go to). As long as you have the "include subfolders" box checked and have started at the right spot, when you then push the NEXT button Win7's Device Manager manual driver install process will scan down from there looking for INF files, and trying to find an INF file which applies to your hardware... namely the Mobility HD 5470.
(8) I have run this 86MB file for the 11.3 version of the Mobility drivers on my own machine, and investigated the self-expanded folders to locate the INF driver file for your chip.
Then I examined the expanded folders, and located the proper INF file for your Mobility HD 5470. Actually, there are two separate INF files and I don't know which one is really the right one, but I'm sure Win7's Device Manager could figure it out correctly.
Anyway, in that expanded \Support folder from running the 86.4MB download "suite" file the true driver files are located in: \Support\11-3_mobility_vista_win7_64_dd_ccc_ocl\Packages\Drivers\Display\W76A_INF
and the two INF files which are pertinent are:CH115930.INF and
C7115930.INF.
Both of these INF files seem to claim that they are the driver files in support of the ATI device whose hardware description is: "ATI Mobility Radeon HD 5400 Series" = ati2mtag_ManhattanP, PCI\VEN_1002&DEV_68E0
"ATI Mobility Radeon HD 5400 Series " = ati2mtag_ManhattanP, PCI\VEN_1002&DEV_68E1
The VEN_1002 designates ATI/AMD.
The DEV_68E0 and DEV_68E1 at the end are the unique identity of your Mobility HD 5470. I don't know why there are two lines, but I'm sure one of them is correct... for your particular hardware.
To be doubly sure that this driver file applies to your hardware, if you look at your currently installed Mobility item under Display Adapters in Device Manager, and right-click on that Mobility item, and select Properties, and then select the Details tab, and then click on the dropdown arrow on the Property item to show the list of all available details, and if you select Hardware IDs, you should see that your currently installed Mobility HD 5470 has either DEV_68E0 or DEV_68E1.
If it does (and it should I'm guessing) then this 11.3 driver update process should absolutely determine that one of the two INF files is the right one, and one of those two lines corresponds to your device, and the update process should proceed successfully.
Just for example, on my own desktop machine with a Radeon HD4850, my "hardware ids" display looks as follows:
You should see something similar under Properties -> Hardware ids for your currently installed Mobility HD 5470.
(9) So back on the screen we were just at, where you've entered the high-level location for where your expanded driver files went and also checked the "include sub-folders" item, when you push the NEXT button the process of manually installing the drivers will truly begin.
It will navigate down to locate those two INF files, and pick the proper one (since it "speaks INF"). It will examine the INF and discover that it applies to your Mobility HD 5470 hardware, and will do the rest of the driver upgrade process.
This should all happen, and complete, automatically and successfully.
If the driver files in that expanded 11.3 folder are really usable for your ASUS-provided Mobility HD 5470 then when it's finished you should be able to right-click on that item (under "Display adapters") and select Properties, and then the Driver tab, and it should show ATI Technologies 3/8/2011, driver version 8.831.2.0.
And that would be a successful driver upgrade.