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We improve the exponent in the finite field sum-product problem from $11/9$to $5/4$, improving the results of Rudnev, Shakan and Shkredov. That is, weshow that if $A\subset \mathbb{F}_p$ has cardinality $|A|\ll p^{1/2}$ then  \[  \max\{|A\pm A|,|AA|\} \gtrsim |A|^\frac54  \] and  \[  \max\{|A\pm A|,|A/A|\}\gtrsim |A|^\frac54\,. \]

Attaining the exponent $5/4$ for the sum-product problem in finite fields