You can use Text entry essay text box type with question, with timing question on the same page and auto advance set to after 300 seconds.

Thank you for your response, much appreciated. I would like the participant to ideally click on a stop watch within the question when they are ready to start writing, which would then count down from 5 minutes. I have seen this in another survey but not sure how to set it up like this?

You need to use custom JS for this.
But, to avoid custom code - in previous page you can put the instruction as - the timer will start when you click next button, so when you are ready to write, click next button.

Thank you very much, is it still then possible for the participant to see the timer?
What is JS? Apologies for the simple questions, I am new to Qualtrics..

For method 1 - JS means Java script, so using java script coding we can put the button on the text entry question page to start a timer and auto advance when 300 seconds are completed.
For method 2- Yes timing question has the feature to show timer, check this resource

Hi Rondev
I have done what you have recommended and it looks good and will work well. Thank you I greatly appreciate your help.