Is it possible for trazodone 50 mg and Ambien (zolpidem) 10 mg to be taken together?

Provider supervision. This combination could be reasonable if you are being closely managed by a health professional prescribing them to you. Treatment decisions are always benefits vs. risks. Ambien (zolpidem) is recommended to be started at 5 mg but can be increased to 10 mg if needed and you are aware of the added risks (see the FDA's warning). I am not sure what other medications you may be taking. Alcohol is not recommended.
Yes. Trazodone can help prolong sleep while Ambien (zolpidem) helps with initial insomnia. Beware of side effects such as postural hypotension, "hang over feelings in the morning. Try to take the Trazodone earlier than your regular sleep time using sleep hygiene,i.e. quiet sleeping area with a comfortable bed, climate control, no exciting TV program before bedtime and even try listening to relaxing music.