By using inotifywait, xwininfo, and xdotool, you can keep watching for directory/file changes and send an F5 key stroke to a selected window (i.e. your browser)
First, create a file called browser_watch.sh with this contents:
SELECTED_WID=$(($(xwininfo | grep "Window id" | cut -d " " -f 4)))
while inotifywait -r -e close_write $file; do
echo "File changed... Sending F5 to window id=$SELECTED_WID"
xdotool windowactivate $SELECTED_WID
xdotool key F5
xdotool windowactivate $CURRENT_WID
Give permissions to this file:
chmod u+x browser_watch.sh
When you run this file, you first will need to click the browser window where the F5 strokes will be sent to.
That is! When a file is changed under the given path, an F5 stroke will be sent to the browser window.