VZ isn't going to invest more into aging copper wiring, that's analog DSL and if OP is getting 5 mb service at his network interface/terminal (re-check those stats. if you have access to the "box" vs. results inside at the RJ-11 and make sure those DSL filters are working optimally) If you still have dial-tone/voice service, listen for any static or noise coming across the receiver. But, it does suggested that you are fairly close to the CO's exchange serving your neighborhood, maybe a mile or less, no more than 1.5 mile (there's a formula to calculate that & VZ can tell you ... it doesn't always run a straight line on its run to your house) Chances are, they might be able to get you better stats. on another new/unused twisted pair of wires at the nearest pole/junction box running down into your home (assumed it's outdoors & overhead) Moisture is the worst enemy for these wiring runs & there might be "taps" (not your "wiretaps") on the line that de-grade the signal over the distance.
Head over to DSLReport dot com as there's VZ-staff who will monitor & run tests on your lines, free-of-charge, and escalate or start a trouble ticket if they find issues - to be dispatched to the field CO's tech folks to follow-up upon, as long as the trouble for any slowdown are not with your inside wiring (it will help if you have inside wiring maintenance plans, etc.)
Otherwise, 10MB speed over cable is relatively slow - especially if you are only getting 4 MB only - these days but it is fine off-peak when most users are not all on the same "node" of shared connections - as otherwise, at dinner time or weekends, you would be luck to get 25% or better of your "provisioned" speed. Again, there are dedicated cable forums on DSLReport dot com - they are pretty good at troubleshooting & making suggestions. Is faster cable speed offered ? Perhaps, you need to "lease" a faster, better & different router from "them" or invest in one of the better ones on your own to get at those faster speed.
We moved into a brand new home 9 years ago here, away from faster 4 - 6 MB reliable DSL speed plans then (and cable) to either expensive cable internet & slow 3 MB (downgraded to 1.5 to 1 MB) pathetic DSL speed as it turned out we're too far from the remote DSL CO - exchange equipment, while waiting for the promised FiOS rollout ... it took a while, and then it stopped around the corners from our city block for another year before we got Fios - and, it's been "sweet" since, for 3+ years now. I think we had 15/5 over cable then but not always at those speed, unless it's late night but it was far superior to DSL.
Now, the slowest recommended plan for Fios here is 50/50 Quantum speed & Time Warner Cable is pitching 200 MB Ultimate plan as many ex-cable users, including viritually everyone on our block - have switched to FiOS, easily tell by looking at those distinctive "boxes" on the side of the buildings & houses.
Perhaps, the FAQ's and some of the basic info over at DSLReports dot com can be a good refresher on where to start.