It is not hard to write one and if you search this forum there should be at least one example.
Hotscripts is always a good place to look for code with a lot of free ones; I just searched under php for multiple file upload and there are probably a couple there that will do what you want.
All you need is an “Add file” button which calls a function that uses DOM methods including createElement() and appendChild() to add a new file input element. You just need to give each file input element the same name and suffixed with to ensure the file names of the uploaded files are sent to your php script in an array.
There is a free tutorial and example code on w3schools showing how to upload a single file. Then it’s only a few minor tweaks as described above to upload multiple files. The php code handling the uploaded files then just needs to be wrapped in a foreach loop to handle an array of uploaded file names.
I wouldn’t use html5 for this because older browsers won’t support it.