Issues with speed on laptop v. mobile devices

I have a Samsung RV511 laptop connected to my (Cox provided) Netgear CG3000d-RG gateway. When I run a speed test on speedtest.net on my cell phone I'm getting download speeds of 20-35 Mbps. However, running the same test on my laptop I'm getting speeds in the 5-6 Mbps range. I have the Premiere level of internet service, so I should be getting much higher speeds on my laptop. The software version on my gateway is V5.5.7_CPR19c. I can't seem to find out if that's the latest version or not or how to update the version if it isn't.

If anyone has any helpful information, I would appreciate it. I work from home, so the faster my internet connection, the better.

Thanks in advance,
Beardking