Tom buys 5 shirts at $16.20 each, and a pair of jeans for $24.50. The shop has a sale on, and so he receives a $10.55 discount.

Write and solve a numerical expression for how much he spends in total.

To find out how much Tom spends in total, we need to calculate the sum of the cost of the shirts and the cost of the jeans, minus the discount.

The cost of the 5 shirts is 5 * $16.20 = $<<5*16.20=81>>81.
After adding the cost of the jeans, the total is $81 + $24.50 = $<<81+24.50=105.50>>105.50.
Finally, we subtract the discount: $105.50 - $10.55 = $<<105.50-10.55=94.95>>94.95. Answer: \boxed{94.95}.