16 ohm speakers with 5 ohm amp ?

A speaker is an electroacoustic transducer that translates electric current into atmospheric vibrations. Impedance is less important than the spl. Which speaker will sound louder? 8 Ohm / 92db or 16 Ohm / 96db?

Read Art Dudley's review of the little Exposure integrated in the current Stereophile.  Horrible on the 16ohn Altecs; much better on the ?10ohm Devores...

you may be ok regarding damaging equipment, but, that is pushing things beyond normal.

using 8 ohm tap for 16 ohm speakers boosts the midrange frequencies which you may like (voices are here), or want tone controls to adjust things (be conservative).

most pre-amps have simple bass or treble controls, (i.e. not midrange tone controls) and we hear less highs as we age, so boosting highs can be less problematic than boosting bass which is the primary source of room interactions. boosting both bass and treble to balance with midrange is not a situation I would want.

see the graph in this link

http://blog.hughes-and-kettner.com/ohm-cooking-101-understanding-amps-speakers-and-impedance/

excerpt (so don't overdo it)

Case 1: running a 16 ohm speaker with an 8 ohm amp output

With this combination, the voltage at the speaker output will rise, while the current will almost halve. The power will drop, although you probably won’t notice it too much, as this combination will likely increase the mids in your tone. So long as you don’t overdo it – make it a rule of thumb not to connect a speaker with more than double the output impedance of that of the amp – this method can be quite useful, as you can effectively boost the mids in a cab that might otherwise be lacking in this department.

Two things- you may have slightly higher distortion on account of the transformer ringing. Often this is offset by the tubes themselves having lower distortion. You will also get less power.

Mismatching the output impedance of a tube amp with the input impedance of a speaker with an input transformer like an electrostatic will cause a serious shift in frequency response.

What happens when you pair a low ohm amp ( Manley Stingray ipod ) with a high ohm speaker ( Zu Oman/ Spacial M3 or 4 Turbo triode) ? 5 Ohm amp output to 12 to 14 ohm speaker. 

Short answer: nothing. Works fine.

Long answer: Tube amps sometimes have different outputs because of the way they work. They will sometimes have 4 and 8 ohm terminals. Internally these come off different taps of the same transformers. Even in that case you can still run either way, its just that you might notice it sounds a little better one way or the other.

Where problems usually come in is low impedance speakers, because they can result in current draw the amp is unable to deliver. High impedance speakers are like anything else high impedance, very easy to drive. Think inputs to amps, pre-amps, etc that are all in the thousands of ohms. Its the low impedance inputs where you run into compatibility problems.

Keep in mind that in any case speaker impedance is nominal. In other words your speaker is not 12 ohms, its something that varies with frequency, averaging around 12 ohms. But at any given frequency it could be a lot lower. This is the main reason people say to match your amp to your speaker, because if the speaker impedance varies a lot and the amp is poor at remaining stable in that same range you can wind up with problems you can actually hear. Which is after all the bottom line. So you hook it up and if it sounds fine then revert back to the short answer.