Save your money and go for a 3.1 final drive.  My engine has plenty of torque and on 10" tires, is easy to drive around town.  60 MPH = 3400 RPM, a slight drop from 3750 RPM using the 3.44, but noticeable.

It's too bad the 5 speed gearboxes for A-series Minis are oriented to performance applications instead of street. By that I mean the gear ratios are chosen to give an even rpm spread between gears. Good for competition, but limits how tall 5th gear can be. On the current 5-speed boxes, 5th is .882.

Ideally, I'd like to have my cake and eat it too - cracking acceleration in 1st and 2nd gears, and a easy cruising 5th. But if you run a 2.76:1 final drive, 1st and 2nd are neutered because the tall final drive bogs these gears down.

For a 5th gear to match the nice cruising of a 2.76:1 final drive on a 4 speed, you need to run 3.1:1 final drive. But because 1st and 2nd gears of the 5 speed are taller than those of a A+ 4 speed box, running a 3.1:1 FD on a 5 speed gives no real advantage in 1st or 2nd.

Either I'd want a 5 speed with A+ 1st-3rd gears matched to a 3.1 FD, or a 5th gear with a .8 ratio on a 3.4 final drive. It wouldn't be ideal for competition and keeping the engine within a narrow powerband rpm range, but great for the street.

If such a thing could be done, I'd have already bought a 5 speed. But after running the ratios over and over, I just can't see the 5 speed, as they're offered now, actually improving my street driving experience. Especially when considering the cost of same.

Give or take twenty years ago I bought several 5 speeds new in the boxes. I was busy building a street, classic mini.
As much as I wanted fit one in my personal car I had the sinking feeling that just like the JKD dog boxes, spares on
going was going to be an issue.

As I have been reading about the 5 speeds currently out there they suggest not using with a turbo. I'm not sure I'd
want one under my autocross engine.

In the mid to late 70s I was an active SCCA Solo 2 A S/P competetor in a 67 Cooper S. I managed a 3rd in NE/Div, 1st
SE/Div and a 5th Nationals. Power by a 1330 Cooper S, 13.3 to 1 CR, SC/CR 4 synchro, open diff with 4.35 CWP. Rolling
on 6X10 Revs with gumball slicks. Weber 45 DCOE and straight exhaust with megaphone.

As for street mini I also like the idea of low RPM producing high MPH. I have been running and building ultra wide ratio
gear sets with 2.76 CWP and two O/D drop gears. Ends up with 69 MPH at 3000 RPM. With 145/10s or 145/12s wheel
spin in first is a issue. I have one in my car and three in customer cars. Engines are built for torque 1000-4500 as
there is a 1000 RPM drop with each up shift. I currently have the parts to assemble another tranny or complete power unit. 

I also have SC/CR 4 synchro, standing start JKD involute dog box NOS with shift forks. A NOS Swift rolling
start dog box set with forks for rod change and lay gear shaft. I also have cross pin diffs, Tranex posi and some
posi CWP sets. If you want something special in a tranny contact me. Steve (CTR)

I know how to get a 5 speed into a Mini. Of course it's attached to a Honda engine.....

I considered a 5-speed in the early stages of my restoration. After reading several posts on different forums including a video from Jamal, I concluded they were a bit wonky. I passed. Perhaps if I heard from folks who were happy w/ their 5-speed I might reconsider. It sure would be sweet cruising at 65 mph @ 3200 rpm.

A standard diff has 4 tapered gears in a circle, two of which connect to the output shafts. The two other gears (If I recall correctly) are kept in alignment opposite each other with a straight shaft or 'pin'. Under heavy use they wear or break. A cross-pin has 4 ends instead of two, and keeps all four gears properly aligned, providing better transfer of force and a lower likelihood of breakage.
A limited slip diff generally has an arrangement of clutch plates between the output shafts, allowing them to turn at different rates only by slippage.

The cross pin diff is not the same as a limited slip.  Take a look at an exploded diagram of the differential and you will notice the standard configuration has 2 spider gears.  The cross pin diff uses a couple of new/different parts so you can have 4 spiders.

As Chuck said there are a few possible 5-speeds but they are seriously expensive. 

Well I should have just looked myself but thanks.  So what is a X pin differential?  Is that what we would call Limited slip?

If I ever get to run an autox this summer I'll find out if the rear sway bar helps keep the right front tire down.  If so I might just start saving for that 5 spd.

I'm having a 5 spd TREMEC put into my 65 corvette next week so that will spoil me for sure.

A SEARCH for PARTS here will get you at least three.

Yes, MiniSpares sells a 5 speed gearbox, you can spec the diff ratio and whether you want a crosspin diff or a limited slip. I know of a couple of people that have them and really like the extra gear for highway cruising.

I guess I have to specify that as the newer Bini's probably have them.  
So is there a modification, upgrade, to install a 5 speed in the classic??  I would even consider a limited slip, after I run this new sway bar at an autox.