There are at least four factors:
1) Physical durability (which in turn depends on how you treat it, and the quality of the machine to begin with.)
2) The generation/age of the hardware (which goes obsolete over time, as software gets more demanding; some parts of that can be upgraded and some can't)
3) The aging of the Windows or other OS installation (which depends on how much you install or uninstall stuff, but thanks to security updates, has a finite lifetime no matter what. If you're comfortable manually reinstalling your OS, this is infinitely renewable, but many people aren't.)
4) Battery aging which is mostly a matter of recharge cycles, but being left sitting un-charged for a long time can murder a battery as well. (In most non-Apple machines the battery is replaceable, even if a few screws are involved, but it eventually becomes less than cost effective.)

As for the times that are typical:
1) For a very heavy user, I'd expect 1-3 years out of a low-end consumer machine, and 3-5 years out of a high quality business machine. For an abusive one, except for ruggedized machines these can be much lower. For a light user, most machines will be obsolete in other senses long before they wear out physically.

2) These things are generational. The oldest laptops which I'd recommend as really fully useful today would be midrange-to-high end machines using the 2nd Generation Intel Core i5 and i7 processors that came out in April of 2011 ("Sandy Bridge" or i5-2520M.) The 2010-generation Core i5 machines are going to be a significant compromise, but still usable. A 2009 or earlier generation Core 2 machine is basically just fit for very patient people who absolutely cannot afford better. A 2005 or older generation Pentium 4 or Pentium 3 machine is fit only for recycling or a museum.

That said, the fact that we've gotten a little less than 5 years out of a good generation of machines (and probably another 1 or 2 out of those, at that) and almost 6 out of an acceptable one is unusual. The Core 2 generation machines struggled with a lot of the newer software in the late 2000s, and with Windows Vista and later 7 pretty much from day 1, and heavy users saw good reason to upgrade to the i5s pretty much as soon as they came out. So you kind of pay your money and take your chances, and hope that the software stays on a relatively measured cycle rather than making another big jump.

It also depends on how high-end the processor was to begin with; a mid-range (i5 or dual-core i7) or high-end one (quad core i7) is going to stay good a lot longer than a low-end one (Celeron/Pentium/i3 or anything from AMD.) For desktops, lower-end tends to be safer, but for laptops I recommend never buying anything less than an i5 even today.

3) For Windows XP, as a heavy user, I reinstalled roughly every 6 months. With Windows Vista and 7, I was upgrading my machine roughly every 18 months, and typically didn't need to reinstall Windows before the machine was passed on as a hand-me-down, but on desktop machines which last a good bit longer, 18 months to 2 years is good mark for reinstalling Windows if you keep a machine longer.

Because of delays with the new processors and machines, my present machine made it past the two year mark, and after upgrading Windows 8.1 to Windows 10 at around the 18 month mark, I reinstalled Windows 10 a few months later to clean it off.

4) Most lithium-ion batteries last between 250-300 full charge/discharge cycles before it becomes really obvious that there's some wear, and somewhere around 3x that many before they're useless. Only charging them to 90%, and never discharging them fully (say, only down to 10-15%) will extend that life -- and unlike older batteries, a partial charge/discharge has no memory effect and doesn't wear it as much as a full one (although it's not linear -- you're not going to double your cycles by doing a 50% discharge.) Newer machines tend to have better logic about not going to 100% or letting you fully discharge before shutting down, but in practice, if you use it on battery every day, you'll see noticeable loss of battery life before a year is out, and may not get to the three year mark before needing a new battery. For mainly desktop use, the main hazard is leaving it fully discharged for a long time, but I've got 9-year old spare batteries for the Dell D620 that were stored with a 50% charge and which seem fine.

That mainly effects #1 and #4.

"Running very slowly" is rarely a hardware problem, and when it is, it's usually a user repairable one (subset of #1 -- "gunk/dust/hair in the heat sink/fan") or much more rarely one requiring new parts ("the fan died"); more usually it's a "this machine is obsolete" (#2) problem, or a "windows needs to be reinstalled problem." (#4)

In the case of obsolete, it's often the easy upgrade of more memory, and/or an SSD. If it's the processor being outdated, there is generally no practical way to upgrade.

For a 5 1/2 years old, that's probably a 1st-generation Core i machine ("Westmere"/ e.g. an i5-520M) which will still be OK for most relatively patient users, but getting a bit long in the tooth. Heavier users would probably want to upgrade. There were still some Core 2 machines on the market then, and those would definitely be time to replace.

Could you just use it with an external monitor/keyboard/mouse? Is it a business model that is amenable to a docking station?

In my line of work, you still can't buy any laptop that is as powerful as a midrange desktop -- a sub-$1000 quad core desktop i5 machine will outperform a $2000+ Xeon workstation-replacement -- and a true workstation desktop can be as much as 5x more powerful as the most powerful laptops on the market (2x. 10 core CPUs vs. 1x 4 cores.)

If you don't need that kind of power, there's not much reason to go back to a desktop other than cost, and the processors are still basically generational. OTOH, if you use it at your desk a lot, having a laptop that can work with a docking station is a really nice thing.

How did you get a E6410 with an i7-720QM? Manual upgrade with some kind of heat sink mod? Because as far as I know, Dell never offered that machine with a quad-core processor out of the factory, and they really weren't built for a 45W CPU rather than the regular 35W dual cores.