Just because a specific "extension link" doesn't work doesn't mean you cannot save ZEE5 videos. Here are three reliable methods:
If you reject the official app and cannot find a safe Chrome extension, you have two remaining options that are technically superior to any extension.
The short answer is: Rarely, and usually poorly.
Chrome extensions are small software programs that modify your browser. A "zee5 video downloader chrome extension" claims to sniff out the video stream (usually an M3U8 or MP4 file) and save it to your hard drive.
Why most of them fail: