How can I measure voltage in range -15 V to 50 V with an ADC in a microcontroller in a single circuit arrangement for scaling?
You can translate and scale with just three resistors. This is a clever method to calculate them, which you almost can do without calculator.  

Use a pull-up to \$+5V\$ and and a pull-down to \$GND\$. Then we have  

  

(Olin, I borrowed your schematic. I hope you don't mind!)  

We'll consider two situations: one with \$V_{IN}\$ = \$-15V\$ and one with \$V_{IN}\$ = \$+55V\$.
We'll have a set of two equations, so we can choose 1 resistor value. Let's take \$30k\$ for \$R2\$.

First. \$V_{IN}\$ = \$-15V\$. The ADC should then be at \$0V\$. That means that there won't be any current through \$R3\$, since there's no voltage difference. Then \$R2\$ and \$R1\$ form a voltage divider with  

\$ \dfrac{0V - (-15V)}{R2} = \dfrac{5V - 0V}{R1} \$

or

\$ R1 = \dfrac{5V}{15V} \cdot  30k\Omega = 10k\Omega \$  

Found our first value.  

Then the second situation. \$V_{IN}\$ = \$+55V\$. The ADC should then be at \$+5V\$. That means there won't be any current through \$R1\$, since there's no voltage difference. Then \$R2\$ and \$R3\$ form a voltage divider with  

\$ \dfrac{55V - 5V}{R2} = \dfrac{5V - 0V}{R3} \$

or  

\$ R3 = \dfrac{5V}{50V} \cdot 30k\Omega = 3k\Omega \$  

Found our second value. So  

\$R1\$ = 10k\$\Omega\$,
\$R2\$ = 30k\$\Omega\$,
\$R3\$ = 3k\$\Omega\$.

edit
Olin suggests something about the impedance the ADC expects. Let's look at a random microcontroller's datasheet and see what it says:  


  "The ADC is optimized for analog signals with an output impedance of approximately 10 kΩ, or
  less. With such sources, the sampling time will be negligible." (p.90)


The output impedance of the network is the parallel of \$R1\$, \$R2\$ and \$R3\$, so we can immediately see that it fulfills the requirement. If it wouldn't have, we'd have to scale the resistors down, keeping their ratios equal until  

\$ \dfrac{1}{R1} + \dfrac{1}{R2} + \dfrac{1}{R3} &gt; \dfrac{1}{10k\Omega} \$    

The only thing remaining is check for tolerances. The divider will give exactly us \$0V\$ for \$-15V\$ in if the resistor values are exact. You can buy 0.1% resistors (still affordable) or even 0.01% (more expensive) and you'll be fine.
But you can also use standard 1% resistors. Increasing \$R2\$ a bit means that the input voltage won't pull as hard up or down, and you'll stay away from the ADC's limits. If you choose 31k\$\Omega\$ instead of 30k\$\Omega\$ the ADC range will change to 0.03V to 4.88V, that's &lt;1% and 2.5% Full Scale. Even with worst case tolerances you'll remain in the ADC's measurement range.