What’s the difference between 二五 and 二十五? Can I just say 二五 when I’m talking or counting instead of 二十五? Will it make a difference between the two of them? Or is it because 二五 is like everyday speech (informal) and 二十五 (formal) for writing?
I watched 奔跑吧第 “Keep Running” show in order to learn and improve my chinese. I remembered in one of the episode of the show, the members were counting without 十 between numbers. I’m trying to learn the “everyday” chinese by watching chinese dramas and variety shows in order to improve my comprehension and speech.
the members were counting without 十 between numbers.

This is exactly where the &quot;十&quot; can be completely omitted, when one is counting. It is quite normal to omit the &quot;十&quot; after passing 20 when counting, especially when one is counting fast.
I cannot recall other circumstances when the &quot;十&quot; can be omitted.
Also, one might drop the hundred part completely after 100, starting from 一 again. The hundred part is may be only included when a whole hundred is reached. E.g. 九七, 九八, 九九, 一百, 一, 二, 三, 四, ......, 九七, 九八, 九九, 二百, 一, 二,  三, 四, ...... The hundred part is memorized instead of spoken out. (Sometimes one might use fingers to keep track of the number of hundreds)
Disclaimer: I am a native Chinese speaker in Beijing. This may differ in different regions or in different dialects.