In MT5, press F4, or go to Tools → MetaQuotes Language Editor, to open MetaEditor.
In MetaEditor, click File → New, choose Expert Advisor (template), click Next, and name it EURUSD_Engulfing_EA. Click Next and Finish.
Select everything in the new file (Ctrl+A) and delete it.
Open EURUSD_Engulfing_EA.mq5 from the download in Notepad. Select all, copy, and paste it into MetaEditor.
Press F7 to compile. It should say "0 errors".
Go back to MT5. Press Ctrl+N to open the Navigator, expand Expert Advisors, and drag EURUSD_Engulfing_EA onto an EURUSD chart. If it isn't listed, right-click and choose Refresh.
Make sure the Algo Trading button in the top toolbar is green. On the EA's Common tab, tick "Allow Algo Trading".
If you also can't open MetaEditor, or you're using the MT5 phone app or web version, tell me. The phone app can't run EAs at all, so you'd need MT5 on a laptop or PC.
If the compile step shows any errors, paste them here and I'll fix them.