It would be most helpful if you would screenshot the setting dialog in chirp and include that, but I’ll try to do this from memory. There’s about a 50/50 chance of me making a mistake .
You need to tell Chirp that it’s two different tones and then the RX Tone is blank. That requires setting three different columns.
First is Tone Mode, which is set to Cross.
Second is Rx Tone or RX CTCSS or RX DCS, which you leave blank.
Third is Cross Tone, which is set to CTCSS—> if you need a CTCSS Tone for transmit, or DCS—> if you need to transmit a Dcs Tone. Because the second part (after the arrow) is blank, you have no receive tone.
If that doesn’t help I’ll take a look at your screen shot in the morning and try to figure out what I said wrong.
Now if you want to do it from the front panel, I think you change it from Tsql to just Tone and it won’t look for a receive tone, but it has been a while since I programmed a UV5R.