Is sulfamethoxazole/TMP effective against gonorhea and chlamydia?

Sulfamethoxazole/TPM would be ineffective against gonorrhoea and chlamydia.

Chlamydia is caused by the bacteria Chlamydia trachomatis.
Chlamydia can be treated with a variety of antibiotics, including azithromycin, tetracyclines, quinolones, and erythromycin.

Gonorrhea is caused by the bacteria Neisseria gonorrhoeae. Penicillin use to be given but the bacteria have become resistant to it. Flouroquinolones are also used but resistance is also beginning. Antibiotics called cephalosporins are now the drugs of choice eg Ceftriaxone or alternatively Azithromycin (Zithromax).

For more information visit:
https://www.drugs.com/health-guide/chlamydia.html
https://www.drugs.com/health-guide/gonorrhea.html