The LF353 is very similar to the TL072.
That circuit will work, but might need improvement.
What's the lowest frequency of interest? the input impedance of your circuit is R4||R3, which is 2k35, giving a lower cut-off frequency of F =1/(2pi*RC) = 1/(2pi*2350*1*10
-6) = 68Hz.
If you want more bass response you could increase R4 & R3 considerably. The LF353 is a FET input op-amp with very low bias currents and a huge input impedance, so much higher value resistors can be used.
Consider increasing the value of C1, for more bass response.
R5 doesn't do anything. The gain is unity.
How smooth is the 12V rail? You might want to bypass R3 to 0V with a capacitor and connect it to the +input, via another resistor.

Oh, I'm not quite sure what that means. What would be the correct way to set it up for a small gain of say 5?
By using a non-inverting amplifier circuit. The top-right hand one in the schematic below:
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Credit: audioguru for originally making this schematic.
Gain = 1 + R1/R2