Your principal will last indefinitely if your interest rate (or equivalent) is at least 10%. Otherwise, spreadsheets come in very handy for these sorts of questions.
Here are some formulae you can use, assuming your interest comes in at the end of the year as a lump sum and you draw your expenses immediately upon receiving the interest:
First row: Year (Y=2018 or current year), Principal amount (P=100,000), Rate of change (R=1.05 for 5% interest), Amount Drawn (D=10,000), Balance (B=PR-D).
Subsequent rows (referencing the variables in the row before it): Y+1, P’=B, R, D, P’R-D.
Look down to the row where the Balance column is first negative. The first column (year) tells you the year that the funds run out.
Once you’ve set up your spreadsheet, you can change the interest rates or drawings for particular years or year ranges.
Here's a snapshot of the above spreadsheet using the given parameters ($100k principal, 5%pa interest, $10k drawn each year), showing the funds lasting for 14 years and running out in the 15th year: