What circuit can be used to match input to output voltage by using an opamp?
One topology that works in general is to create a standard differential amplifier setup using two pars of resistors having the same ratio.

Let...
VIL = the lowest input voltage
VIH = the highest input voltage
VOL = the desired output voltage when the input is VIL
VOH = the desired output voltage when the input is VIH

Configure the gain to be...
G = (VOH - VOL) / (VIH - VIL).

The resistors are set such that...
R2 / R1 = G

A reference offset voltage VREF is chosen such that...
VREF = VOL - G * VIL

VREF can be derived either from a dedicated buffered reference voltage or a Thevenin equivalent circuit whose output impedance is equal to R2.  For example if R2 were 100K and you needed the offset to be 2.5V and you had a 5V supply; then you could split R2 on the positive side into two 200K resistors (one attached to 5V and the other to GND)

The circuit is shown below...







simulate this circuit &ndash; Schematic created using CircuitLab

NOTE:  If you need G to be negative then you can put the input on the negative side R1 and put GND on the positive side R1.  If you need the input to be differential then connect the positive and negative sides of the differential signal to the pair of R1s.

For your specific case you need a gain of 8V / 5V.  You can use...
R1 = 4.99K
R2 = 8K = 7.5K + 499 ohms

To make an offset of 7V you have two options.
1)  Make a regular voltage divider and buffer it with an op amp setup as a voltage follower.  The obvious choices for the divider are 8K (7.5K + 499) and 7K (6.98K).

2)  Use a pair of resistors that form a 7V voltage divider with 15V, and have a parallel output impedance of 8K.  For this approach we have two equations and two unknowns..
EQ1:  1 / R2a + 1 / R2b = 1/R2

EQ2:  VCC * R2a / (R2a + R2b) = VREF

Solving both equations gives...

R2a = R2 * VCC / VREF = 8K * 15V / 7V = 17.14K.

R2b = R2 * VCC / (VCC - VREF) = 8K * 15V / (15V - 7V) = 15K.