To simplify this expression, we need to factor the numerator and denominator and then cancel out any common factors.

Numerator:
10a² - 6a + 5ab - 3b
Factor out common terms:
2a(5a - 3) + b(5a - 3)
Factor by grouping:
(2a + b)(5a - 3)

Denominator:
5a² - 8a + 3
Factor out common terms:
(5a - 3)(a - 1)

Now we can rewrite our expression as:
(2a + b)(5a - 3)/(5a - 3)(a - 1)

Since there is a common factor of (5a - 3) in both the numerator and denominator, we can cancel it out:
(2a + b)/(a - 1)

Therefore, the simplified expression is:
(2a + b)/(a - 1)