Worksheet functions were not designed for this. User-defined worksheet functions were not made a feature of Excel to go and fetch data online - in my humble opinion, this is a terrible abuse of UDF's.

A function like this should be part of the definition of a class module that defines an object responsible for this task, and wrapped with an interface, say ITickerPriceProvider:

Public Function GetTickerPrice(ByVal ticker As String) As Double
End Function

Then your code moves into a class module with Implements ITickerPriceProvider, and the signature becomes this:

Option Explicit
Implements ITickerPriceProvider

Private Function ITickerPriceProvider_GetTickerPrice(ByVal ticker As String) As Double
    'your code
End Function

What gives? Now you can get fancy and write a macro that looks like this:

Public Sub UpdateTickerPrices()

    Dim provider As ITickerPriceProvider
    Set provider = New WebTickerPriceProvider
    
    Dim updater As TickerSheetUpdater
    Set updater = New TickerSheetUpdater

    updater.UpdateTickerPrices provider, TickerPricesSheet

End Sub

And the TickerSheetUpdater.UpdateTickerPrices method is where you go and implement the code that locates ticker strings (your worksheet must have a column with those, right?), fetches the prices for each one, and updates the worksheet.

This is a job for a macro, not a UDF.

As a bonus, your code can be unit-tested - and now if somebody cuts the network cable, you can handle errors gracefully, instead of having 200 UDF calls blowing up one after another.

As for the implementation itself, I don't see any glaring issues. I would have named IE something like browser, URL would have been url, and there would have been an On Error GoTo CleanFail statement at the top, and a CleanExit label to ensure resources get cleaned up whether or not an error occurs:

Private Function ITickerPriceProvider_GetTickerPrice(ByVal ticker As String) As Double
    On Error GoTo CleanFail

    'implementation here

CleanExit:
    Set browser = Nothing
    Set pageData = Nothing
    Exit Function

CleanFail:
    'handle errors
    Resume CleanExit

End Function

Turning ScreenUpdating off isn't going to help much, at least not with a UDF approach - the function isn't updating any cell values, it is a cell value.

However I'd try to see if there wouldn't be a way to remove this:

Application.Wait Now + TimeSerial(0, 0, 5)

...or add a comment that explains why it's needed, and why it needs to be a whole 5 seconds - especially given you've just waited for a specific ReadyState on your IE object:

 Do Until IE.ReadyState >= 4
        DoEvents
 Loop

What's 4 anyway? Make an Enum for the possible values, and use it instead of hard-coding a value like this. Why do you need to wait 5 seconds after the browser gets into that ReadyState? Could you keep loop-waiting for a later state value? An enum would help understanding what's going on and why here.