buck dc dc step down with LT1054C
It looks like you are missing the R1/R2 resistor divider network used to set the desired output voltage for the voltage converter.  From the LT1054 datasheet section 8.2.2.1 (http://www.ti.com/lit/ds/symlink/lt1054.pdf):

The error amplifier of the LT1054 drives the PNP switch to control the
voltage across the input capacitor (CIN), which determines the output
voltage. When the reference and error amplifier of the LT1054 are
used, an external resistive divider is all that is needed to set the
regulated output voltage. shows the basic regulator configuration and
the formula for calculating the appropriate resistor values. R1 should
be 20 kΩ or greater because the reference current is limited to ±100
μA. R2 should be in the range of 100 kΩ to 300 kΩ.

The typical application circuit at the top of section 8.2 shows where resistors R1 and R2 should be placed:

Edit 1
Followup on your other thought, the electrical characteristics section of the datasheet specifically calls out using tantalum capacitors for Cin and Cout, so I think you're fine using that type rather than Al.

All regulation specifications are for a device connected as a
positive-to-negative converter/regulator with R1 = 20 kΩ, R2 = 102.5
kΩ, external capacitor CIN = 10 μF (tantalum), external capacitor COUT
= 100 μF (tantalum) and C1 = 0.002 μF

Edit 2
Two other ideas:

The datasheet makes specific mention that when using the LT1054 as an unregualted inverter, equal nominal values should be used for Cin and Cout for best results (Capcitor Selection https://www.analog.com/media/en/technical-documentation/data-sheets/1054lfh.pdf)

I suspect that when configured in an unregulated circuit the LT1054 can't effectively invert voltages lower than 7V.  There are other application circuits like the positive doubler which accept voltages as low as the minimum Vin of 3.5V, but all of the electrical characteristics for -5V regulated output are measured with Vin from 7-12V.  If you use the resistor divider values for -5V regulated output and a Vin of 7V or higher, do you see a regulated -5V out?