what is the algebraic expression for the product of 2 times a and 5 times b?

It is not clear to me what you are doing.

I think it is 2a*5b

To find the algebraic expression for the product of 2 times "a" and 5 times "b", you can multiply the two terms together.

The product of 2 times "a" can be written as 2a. Similarly, the product of 5 times "b" can be written as 5b.

So, the algebraic expression for the product of 2 times "a" and 5 times "b" is 2a * 5b, which can also be simplified as 10ab.