Your confusion comes from how you're using the term download speed. There are actually two factors that influence a connection's actual download performance:
- Bandwidth: The maximum speed at which a connection can move data
- Throughput: The actual amount of data being transmitted successfully at a given moment
Think of your network connections as water pipes. Your LTE connection is a pipe that can move a maximum of 30 MegaBits Per Second (Mbps). Obviously your LTE connection's pipe is bigger than your Wi-Fi so it has the potential to download data faster. But if data is coming from the remote server at only a trickle (e.g. at a rate of 5 Mbps), having a bigger pipe doesn't make a difference.
Your connection to a remote server on the Internet is like a series of multiple pipes of all different sizes. As with real water pipes, the rate ("speed") at which data arrives at your end of the link is constrained by the smallest pipe in the link. If you and the server both connect to the Internet with 30 Mbps pipes, but one of the connections between you is only moving data at a rate of 5 Mbps, then data will be downloaded on your end at 5 Mbps, not 30 Mbps.
In your case it's possible the complete link to the remote server through your Wi-Fi connection has no bottlenecks and data can move at the full 5 Mbps. The LTE connection may be restricted at some point along the way such that you're not able to achieve even 5 Mbps of throughput. There are many reasons for this, such as bandwidth limits enforced by your LTE provider, faulty equipment, etc.