Conditions 1-5

Condition 1: Islam

The opposite of disbelief. If the one who insults Allah or worships
other than Him and prays, the prayer is invalid unless s/he repents.

Condition 2: Sanity

The opposite of insanity. Likewise, being intoxicated

Condition 3: Tamyeez

It does not mean puberty. Its meaning is differentiating between
things; one knows the question and the answer. There is no specific
age. Usually it is 7 years old. When is the prayer of the child valid?
If the child is able to differentiate, otherwise prayer is invalid.

Condition 4: Wudoo