Bottlenecks and busy times
The upload and download speeds given by a speed test do not necessarily mean that you will get anything near that in point-to-point communications. If your data has to take several hops, or go trans-Atlantic or trans-Pacific, your point-to-point route could be limited by any number of bottlenecks along its path. And, there may be certain times of the day when you get slower speeds, which could also be due to the route your data takes.
Speed, Latency, and Stability
The maximum speed you can get is based on a combination of bandwidth, latency (ping value), and connection stability. The farther you move from the Slingbox, the greater your latency. With growing latency, the maximum speed drops. And with insufficient speed, the stability drops.
Aside from latency, you might be suffering from sub-optimal routing. Try signing up for a VPN or proxy service and connecting to a server between your Slingbox and your player to influence the route taken. Your ISP might be throttling or blocking your traffic in either location, and it's possible that a VPN could remedy this.
Bear in mind that VPNs and proxies can also make things worse. You need to find one that isn't overloaded, has good connections to the Internet backbone, and is one that is known as "tier one" because the provider owns and manages its own equipment.
UPnP and Port Forwarding
One last thing to check: a Slingbox uses various streaming methods, including TCP, RELAY, or SNATT. TCP is the recommended streaming method, not only for speed, but for stability as well. To enable TCP streaming, you must enable Universal Plug and Play, or UPnP on your router, or set up port forwarding correctly.
Most routers these days have UPnP enabled by default. However, if you need to enable UPnP, you must access your router admin page, usually via your browser (see your router documentation if you aren't sure). If this doesn't work and you're using a Slingbox 350, Slingbox M1/M2, or SlingTV/Slingbox 500, follow the steps in the article below entitled, "What if automatic router setup doesn't work?."
If you are using an older Slingbox, you may need to manually configure you router. See the article linked below for more information.