Dropbox offers 2GB of storage for free, OneDrive offers 5GB, and Google Drive provides free users with 15GB.
Many people use two or more cloud storage accounts to take advantage of their free storage plans or to use one for work, one for personal use, and another for friends and family. Thats been fixed in 4.34.x, which is currently rolling out to production. There are numerous cloud service to choose from but most prefer OneDrive for its Windows and Office 365 integration, Google Drive for its Android and Google support, and Dropbox for its streamlined approach across operating systems and its ease of use. It was a bug that the video was allowed to be sent at all. Essentially, all you need to do is upload your files to a folder in your cloud account and then share the link to that file or folder in an email or direct message with your contact. The process for how to share large video files via a cloud service is almost identical regardless of what platform you decide to use.
OneDrive often requires manual syncing to transfer files. Dropbox's 2GM free limit won't be enough for those with a lot of video files.