I learned about the correct play through a professional go player. The wrong paths were filled in by me though, so if I missed something, let me know.
(;AB[qq]AB[qr]AB[pr]AB[qo]AB[ro]AW[sq]AW[po]AW[pp]AW[pq]AW[or]AW[nq]AW[qn]AW[rn]AW[pn]C[T5 should have been White's play. If White tries this, what can Black do?]AP[goproblems]
(;B[sr];W[rr]
(;B[rq];W[ss]
(;B[sp];W[qp]C[Please refrain from unnecessary moves.]
(;B[rs];W[qs]
(;B[ps]C[Black lives in double ko!RIGHT])
(;B[sr]C[Black can live in double ko. If you played this, you either misclicked or thought the only option for black was to play out a ko fight.]))
(;B[sr]C[Black can live in double ko. If you played this, you either misclicked or thought the only option for black was to play out a ko fight.])
(;B[rp];W[ps]C[Ko for life. You can do better.])
(;B[ps];W[rs];B[qs];W[rp];B[sr];W[rs])
(;B[qs];W[sr]))
(;B[rs];W[qs]
(;B[ps];W[so]C[]
(;B[sp];W[rp];B[rs]C[Ko for life. You can do better.])
(;B[rs]C[Ko for life. You can do better.]))
(;B[sp];W[ps];B[sr]C[Ko for life. You can do better.])))
(;B[rs];W[rq]
(;B[rp];W[ss]C[Ko for life. You can do better.])
(;B[sp];W[ss]C[Ko for life. You can do better.]))
(;B[sp];W[rq]
(;B[rs];W[ss])
(;B[qp];W[ps]
(;B[rs];W[ss])
(;B[qs];W[os];B[rs];W[ss]))))
(;B[rq];W[sr]
(;B[sp];W[qp];B[ps];W[rs];B[rr];W[rp];B[ss];W[sr])
(;B[qp];W[so];B[sp];W[rp]C[Ko for life. You can do better.])
(;B[rp];W[ps])
(;B[so];W[qp];B[rp];W[ps]))
(;B[rp];W[ps]
(;B[sr];W[rr];B[rs];W[ss]C[Ko for life. You can do better.])
(;B[qs];W[so]
(;B[rq];W[sr])
(;B[sp];W[qp])))
(;B[qp];W[so]
(;B[sp];W[rp]
(;B[rq];W[sr];B[sp]C[Ko for life. You can do better.])
(;B[sr];W[rr];B[rq];W[ss];B[sp]C[Ko for life. You can do better.]))
(;B[rq];W[sp])
(;B[sr];W[sp]
(;B[rs];W[rq])
(;B[rq];W[rs])))
(;B[sp];W[qp]
(;B[sr];W[rp]
(;B[rq];W[rs])
(;B[rs];W[rq]))
(;B[rq];W[sr];B[ps];W[rs];B[rr];W[rp];B[ss];W[sr]))
(;B[rr];W[so])
(;B[so];W[qp])
(;B[rs];W[sr])
(;B[ps];W[so];B[sr];W[rs]))