Assuming this sample of helium gas behaves like an "ideal gas", the equation PV=nRT describes the relationship between pressure, volume and temperature (for a given number of moles, n).
P = 75 mm Hg
V = 521 L
T = 18 C + 273 = 291 K
R = 62.4 mm Hg L/mol * K (be sure your units for this constant match the units in P, V and T)
P1 x V1 = n x R x T1 and P2 x V2 = n x R x T2
n = assume moles of gas do not change when temp increases from 18 to 23 C. Thus, n = 1 or is omitted.
P1 x V1 = R x T1 and P2 x V2 = R x T2
The problem states that volume changes with the temperature. So, we assume pressure will remain constant, i.e., Charles Law:
V1 = R x T1 and V2 = R x T2
Since R1 and R2 are the same we have a common relationship:
V1/T1 = R and V2/T2 = R
V1/T1 = V2/T2 (also known as Charles Law)
Since we are solving for V2 we isolate that term:
(V1/T1) x T2 = V2
V2 = (521 L x 296 K)/ 291 K
V2 = 530 L
Answer check: Since temperature increased 1.02 % (296K/291K), so must the volume (530 L/521 L) = 1.02 %.
