The 5th edition has a unique ISBN (e.g., 9780194524234 for the Student’s Book). Search that number on legitimate second-hand book sites.
Do not search for "headway elementary 5th edition pdf free download." Instead, search for "Headway Elementary 5th edition Google Drive" (often shared in study groups) or use the official 30-day free trial of Oxford’s digital platform. If that fails, fall back to the 4th edition PDF (easier to find legally as an abandoned copy) and supplement it with modern YouTube grammar lessons.
If you are determined to learn, but cannot afford the official digital version, here is a strategic roadmap using legal "freemium" resources.