With an inverting amplifier, the input to the inverting amplifier and input to the op amp are not the same thing.
See the attached schematic. -15V is applied to the input, +15V at the output, and the op amp only sees 0V and +15V. Remember that the op amp tries to make both inputs equal - by applying the opposite voltage to the other end of a voltage divider, the center will be zero.
Of course, using different resistors can scale the -15V to something under 5V. If you use R1=75k and R2=20k, than -15V becomes 4V.
One bad side to this approach is that the op amp will be unhappy if accidentally powered down. The LM324 is unique in being able to handle inputs up to +32V even when not powered, but that does not apply for negative inputs, only positive.