I'm not overly familiar with the (h,k,l) calculations. I'm actually just learning them myself but everything looks good to me. You however have made a math error:
1dhkl2=h2a2+k2b2+l2c2
(dhkl)2≠a2h2+b2k2+c2l2You can't simply invert both sides of the equation like this with addition of fractions. It'd be like saying:
11=13+13+13
11≠31+31+31If you correct this error you'll get 5.30Å in agreement with your friend. Hope that helped but given the delay I suspect you've already figured the issues out by now.