It very much depends upon the operating mode of the relay board.
If your diagram is correct then it would suggest you need to supply a voltage to the In pins and the board has a common ground, in which case no you can't use a uln2803 as that chip provides a ground on each output that is switched by the corisponding input.
And no ware in the linked page can I see any reference to the board operating at 5V further more the board does not apear to have a 5V regulator on board which suggests the entire board operates at 12V.
You will need to use a 2 transistor driver circuit for each input to the relay board if the above is true,
I would suggest you test the boards operation before proceeding by connecting 12V power supply to vcc and ground, then try connection 12V to an In pin and see if the relay works.
Last edited by pcmanbob
on Sat Nov 16, 2019 9:27 pm, edited 1 time in total.
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The use of crystal balls & mind reading are not supported